% DIAGRAM MACROS (version 3.1)
\catcode`\@=11
%%%%% FIXING SOME PARAMETERS
%%% Fixing the printerresolution
%%% unit = 1 dpi
\newcount\printerresolution
\global\printerresolution=300
%%% Fixing the length of a segment in an arrowhead
%%% unit = 0.01pt
\newcount\headsize
\global\headsize=450
%%% Fixing the thickness of an arrowhead
%%% value = 1/5 of the font size
\font\dotfont = lcircle10 at 3pt
%%% Fixing the distance between the two heads of an epimorphism
%%% unit = 0.01pt
\newcount\epihead
\global\epihead=200
%%% Fixing the default scaling factor for diagrams
\newcount\defaultscale
\def\setdefaultscale#1{\global\defaultscale=#1}
\setdefaultscale{100}
\newcount\actualtextarrowspace
\newcount\actualtextarrowlength
% \computetextparameters computes the parameters
% required to design a text arrow
\newcommand{\computetextparameters}%
{\global\actualtextarrowspace=\textarrowlength%
\global\advance\actualtextarrowspace by 3%
\global\actualtextarrowlength=\textarrowlength%
\global\multiply\actualtextarrowlength by 100}
%%% Fixing the default length of text arrows
\newcount\textarrowlength
\def\settextarrowlength#1{\global\textarrowlength=#1%
\computetextparameters}
\settextarrowlength{20}
\newcount\actualdisplayarrowspace
\newcount\actualdisplayarrowlength
% \computedisplayparameters computes the parameters
% required to design a displayed arrow
\newcommand{\computedisplayparameters}%
{\global\actualdisplayarrowspace=\displayarrowlength%
\global\advance\actualdisplayarrowspace by 3%
\global\actualdisplayarrowlength=\displayarrowlength%
\global\multiply\actualdisplayarrowlength by 100}
%%% Fixing the default length of displayed arrows
\newcount\displayarrowlength
\def\setdisplayarrowlength#1{\global\displayarrowlength=#1%
\computedisplayparameters}
\setdisplayarrowlength{30}
% ERROR MESSAGES
% Checking the next token without gobbling blanks
\def\@ifnexttok#1#2#3{\let\@tempe #1\def\@tempa{#2}\def\@tempb{#3}%
\futurelet\@tempc\@ifntok}
\def\@ifntok{\ifx \@tempc \@tempe\let\@tempd\@tempa\else\let\@tempd\@tempb\fi%
\@tempd}
% \@diagramerror{MSG}{HLP}: Types a Diagram error message MSG and gives an error
% halt with error help message HLP.
\def\@diagramerror#1#2{%
\edef\@@tempc{#2}\expandafter\errhelp\expandafter{\@@tempc}%
\typeout{Diagram error. \space See User's guide for explanation.^^J
\space\@spaces\@spaces\@spaces Type \space H \space for
immediate help.}\errmessage{#1}}
\newif\ifdiagram
% error test and message for text arrows
\def\testtextmode{%
\ifdiagram\@diagramerror{Text arrows are not allowed in diagrams}{Here you
should use east or west diagram arrows, not forward or backward text arrows.
Try proceeding now, typeset could succeed but with unpredictable output.}
\else\ifmmode\relax\else%
\@diagramerror{Missing \string$}{Text arrows should be introduced in math mode.
Try proceeding now, typeset could succeed but output could not be what you expected.}\fi\fi}
% error test and message for diagram arrows
\def\testdiagrammode{\ifdiagram\relax\else
\@diagramerror{Diagram arrows are not allowed in formulas}{Here you
should use forward or backward text arrows, not diagram arrows. Proceeding
could work with unpredictable output, but overflow arithmetic
could also occur.}\fi}
% error test and message for diagrams in math mode
\def\checkmode{\ifmmode\@diagramerror{Wrong mode: no diagrams
allowed in math mode.}{You should leave math mode before
introducing your diagram. All items in the diagram will automatically be
processed in math mode.}\else\relax\fi\global\diagramtrue}
\global\diagramfalse
%%%%% DESIGING THE ARROW HEADS
%%% Customizing the unitlength for the sake of precision
\setlength{\unitlength}{0.01pt}
%%% Printing one dot at the required scale
\def\DOT{{\dotfont q}}
%%% Computing the distance between two dots in an arrowhead
\newcount\basicstep
\basicstep=7227
\global\divide\basicstep by \printerresolution
%%% Computing the number of dots in an arrowhead
\newcount\numberofsteps
\numberofsteps=\headsize
\global\divide\numberofsteps by \basicstep
%%% Producing an arrow head
\newcommand{\makehead}[3]{%
\begin{picture}(0,0)%
\multiput(0,0)(#1,#2){#3}{\DOT}%
\multiput(0,0)(-#2,#1){#3}{\DOT}%
\end{picture}}
%%% Creating bitmap images of the arrowheads
\newcount\xstep
\newcount\ystep
\newsavebox{\northhead}
\savebox{\northhead}{%
\xstep=-\basicstep%
\multiply\xstep by 7071%
\divide\xstep by 10000%
\ystep=\xstep%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\nhead}{\usebox{\northhead}}
\newsavebox{\easthead}
\savebox{\easthead}{%
\xstep=-\basicstep%
\multiply\xstep by 7071%
\divide\xstep by 10000%
\ystep=-\xstep%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\ehead}{\usebox{\easthead}}
\newsavebox{\southhead}
\savebox{\southhead}{%
\xstep=\basicstep%
\multiply\xstep by 7071%
\divide\xstep by 10000%
\ystep=\xstep%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\shead}{\usebox{\southhead}}
\newsavebox{\westhead}
\savebox{\westhead}{%
\xstep=\basicstep%
\multiply\xstep by 7071%
\divide\xstep by 10000%
\ystep=-\xstep%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\whead}{\usebox{\westhead}}
\newsavebox{\northwesthead}
\savebox{\northwesthead}{%
\makehead{0}{-\basicstep}{\numberofsteps}}
\newcommand{\nwhead}{\usebox{\northwesthead}}
\newsavebox{\northeasthead}
\savebox{\northeasthead}{%
\makehead{-\basicstep}{0}{\numberofsteps}}
\newcommand{\nehead}{\usebox{\northeasthead}}
\newsavebox{\southwesthead}
\savebox{\southwesthead}{%
\makehead{\basicstep}{0}{\numberofsteps}}
\newcommand{\swhead}{\usebox{\southwesthead}}
\newsavebox{\southeasthead}
\savebox{\southeasthead}{%
\makehead{0}{\basicstep}{\numberofsteps}}
\newcommand{\sehead}{\usebox{\southeasthead}}
\newsavebox{\eastnortheasthead}
\savebox{\eastnortheasthead}{%
\xstep=-\basicstep%
\multiply\xstep by 9486%
\divide\xstep by 10000%
\ystep=\xstep%
\divide\ystep by -3%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\enehead}{\usebox{\eastnortheasthead}}
\newsavebox{\northnortheasthead}
\savebox{\northnortheasthead}{%
\xstep=-\basicstep%
\multiply\xstep by 9486%
\divide\xstep by 10000%
\ystep=\xstep%
\divide\ystep by 3%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\nnehead}{\usebox{\northnortheasthead}}
\newsavebox{\southsouthwesthead}
\savebox{\southsouthwesthead}{%
\xstep=\basicstep%
\multiply\xstep by 9486%
\divide\xstep by 10000%
\ystep=\xstep%
\divide\ystep by 3%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\sswhead}{\usebox{\southsouthwesthead}}
\newsavebox{\westsouthwesthead}
\savebox{\westsouthwesthead}{%
\xstep=\basicstep%
\multiply\xstep by 9486%
\divide\xstep by 10000%
\ystep=\xstep%
\divide\ystep by -3%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\wswhead}{\usebox{\westsouthwesthead}}
\newsavebox{\westnorthwesthead}
\savebox{\westnorthwesthead}{%
\xstep=\basicstep%
\multiply\xstep by 3162%
\divide\xstep by 10000%
\ystep=\xstep%
\multiply\ystep by -3%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\wnwhead}{\usebox{\westnorthwesthead}}
\newsavebox{\eastsoutheasthead}
\savebox{\eastsoutheasthead}{%
\xstep=-\basicstep%
\multiply\xstep by 3162%
\divide\xstep by 10000%
\ystep=\xstep%
\multiply\ystep by -3%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\esehead}{\usebox{\eastsoutheasthead}}
\newsavebox{\northnorthwesthead}
\savebox{\northnorthwesthead}{%
\xstep=-\basicstep%
\multiply\xstep by 3162%
\divide\xstep by 10000%
\ystep=\xstep%
\multiply\ystep by 3%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\nnwhead}{\usebox{\northnorthwesthead}}
\newsavebox{\southsoutheasthead}
\savebox{\southsoutheasthead}{%
\xstep=\basicstep%
\multiply\xstep by 3162%
\divide\xstep by 10000%
\ystep=\xstep%
\multiply\ystep by 3%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\ssehead}{\usebox{\southsoutheasthead}}
\newsavebox{\easteastnortheasthead}
\savebox{\easteastnortheasthead}{%
\xstep=-\basicstep%
\multiply\xstep by 8944%
\divide\xstep by 10000%
\ystep=\xstep%
\divide\ystep by -2%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\eenehead}{\usebox{\easteastnortheasthead}}
\newsavebox{\northnorthnortheasthead}
\savebox{\northnorthnortheasthead}{%
\xstep=-\basicstep%
\multiply\xstep by 8944%
\divide\xstep by 10000%
\ystep=\xstep%
\divide\ystep by 2%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\nnnehead}{\usebox{\northnorthnortheasthead}}
\newsavebox{\southsouthsouthwesthead}
\savebox{\southsouthsouthwesthead}{%
\xstep=\basicstep%
\multiply\xstep by 8944%
\divide\xstep by 10000%
\ystep=\xstep%
\divide\ystep by 2%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\ssswhead}{\usebox{\southsouthsouthwesthead}}
\newsavebox{\westwestsouthwesthead}
\savebox{\westwestsouthwesthead}{%
\xstep=\basicstep%
\multiply\xstep by 8944%
\divide\xstep by 10000%
\ystep=\xstep%
\divide\ystep by -2%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\wwswhead}{\usebox{\westwestsouthwesthead}}
\newsavebox{\westwestnorthwesthead}
\savebox{\westwestnorthwesthead}{%
\xstep=\basicstep%
\multiply\xstep by 4472%
\divide\xstep by 10000%
\ystep=\xstep%
\multiply\ystep by -2%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\wwnwhead}{\usebox{\westwestnorthwesthead}}
\newsavebox{\easteastsoutheasthead}
\savebox{\easteastsoutheasthead}{%
\xstep=-\basicstep%
\multiply\xstep by 4472%
\divide\xstep by 10000%
\ystep=\xstep%
\multiply\ystep by -2%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\eesehead}{\usebox{\easteastsoutheasthead}}
\newsavebox{\northnorthnorthwesthead}
\savebox{\northnorthnorthwesthead}{%
\xstep=-\basicstep%
\multiply\xstep by 4472%
\divide\xstep by 10000%
\ystep=\xstep%
\multiply\ystep by 2%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\nnnwhead}{\usebox{\northnorthnorthwesthead}}
\newsavebox{\southsouthsoutheasthead}
\savebox{\southsouthsoutheasthead}{%
\xstep=\basicstep%
\multiply\xstep by 4472%
\divide\xstep by 10000%
\ystep=\xstep%
\multiply\ystep by 2%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\sssehead}{\usebox{\southsouthsoutheasthead}}
\newsavebox{\northeasteastnortheasthead}
\savebox{\northeasteastnortheasthead}{%
\xstep=-\basicstep%
\multiply\xstep by 9806%
\divide\xstep by 10000%
\ystep=\xstep%
\divide\ystep by -5%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\neenehead}{\usebox{\northeasteastnortheasthead}}
\newsavebox{\northeastnorthnortheasthead}
\savebox{\northeastnorthnortheasthead}{%
\xstep=-\basicstep%
\multiply\xstep by 9806%
\divide\xstep by 10000%
\ystep=\xstep%
\divide\ystep by 5%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\nennehead}{\usebox{\northeastnorthnortheasthead}}
\newsavebox{\southwestsouthsouthwesthead}
\savebox{\southwestsouthsouthwesthead}{%
\xstep=\basicstep%
\multiply\xstep by 9806%
\divide\xstep by 10000%
\ystep=\xstep%
\divide\ystep by 5%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\swsswhead}{\usebox{\southwestsouthsouthwesthead}}
\newsavebox{\southwestwestsouthwesthead}
\savebox{\southwestwestsouthwesthead}{%
\xstep=\basicstep%
\multiply\xstep by 9806%
\divide\xstep by 10000%
\ystep=\xstep%
\divide\ystep by -5%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\swwswhead}{\usebox{\southwestwestsouthwesthead}}
\newsavebox{\northwestwestnorthwesthead}
\savebox{\northwestwestnorthwesthead}{%
\xstep=\basicstep%
\multiply\xstep by 1961%
\divide\xstep by 10000%
\ystep=\xstep%
\multiply\ystep by -5%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\nwwnwhead}{\usebox{\northwestwestnorthwesthead}}
\newsavebox{\southeasteastsoutheasthead}
\savebox{\southeasteastsoutheasthead}{%
\xstep=-\basicstep%
\multiply\xstep by 1961%
\divide\xstep by 10000%
\ystep=\xstep%
\multiply\ystep by -5%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\seesehead}{\usebox{\southeasteastsoutheasthead}}
\newsavebox{\northwestnorthnorthwesthead}
\savebox{\northwestnorthnorthwesthead}{%
\xstep=-\basicstep%
\multiply\xstep by 1961%
\divide\xstep by 10000%
\ystep=\xstep%
\multiply\ystep by 5%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\nwnnwhead}{\usebox{\northwestnorthnorthwesthead}}
\newsavebox{\southeastsouthsoutheasthead}
\savebox{\southeastsouthsoutheasthead}{%
\xstep=\basicstep%
\multiply\xstep by 1961%
\divide\xstep by 10000%
\ystep=\xstep%
\multiply\ystep by 5%
\makehead{\xstep}{\ystep}{\numberofsteps}}
\newcommand{\sessehead}{\usebox{\southeastsouthsoutheasthead}}
%%% Restoring the standard unitlength
\setlength{\unitlength}{1pt}
% MACROS FOR MARKED ARROWS
\newsavebox{\isomorphismmark}
\newcommand{\isomark}[1]{\savebox{\isomorphismmark}{#1}}
\isomark{$\cong$}
\newcommand{\isosign}{\usebox{\isomorphismmark}}
\newif\ifuserdist
\newsavebox{\distributormark}
\newcommand{\distmark}[1]{\ifx#1\distcircle\userdistfalse\else%
\userdisttrue\savebox{\distributormark}{#1}\fi}
\newsavebox{\distributorcircle}
\savebox{\distributorcircle}{\begin{picture}(0,0)%
\put(0,0){\circle{4}}\end{picture}}
\newcommand{\distsign}{\ifuserdist\usebox{\distributormark}\else%
\usebox{\distributorcircle}\fi}
\userdistfalse
% MACROS FOR ADJUSTING THE LENGTH OF MONOMORPHISMS AND EPIMORPHISMS
\newcount\monolength
\newcount\epilength
\newcount\bimolength
\newcount\secondmonolength
\newcount\secondepilength
\newcount\monotail%
\global\monotail=\headsize%
\global\multiply\monotail by 7070%
\global\divide\monotail by 10000%
\newcount\truemonotail%
\newcount\trueepihead%
\def\truetail{\truemonotail=\monotail%
\multiply\truemonotail by 100%
\divide\truemonotail by \SCALE}
\def\truehead{\trueepihead=\epihead%
\multiply\trueepihead by 100%
\divide\trueepihead by \SCALE}
\newcount\Monotail%
\global\Monotail=\headsize%
\global\divide\Monotail by 2%
\newcount\Epihead%
\global\Epihead=\epihead%
\global\multiply\Epihead by 7070%
\global\divide\Epihead by 10000%
\newcount\Truemonotail%
\newcount\Trueepihead%
\def\Truetail{\Truemonotail=\Monotail%
\multiply\Truemonotail by 100%
\divide\Truemonotail by \SCALE}%
\def\Truehead{\Trueepihead=\Epihead%
\multiply\Trueepihead by 100%
\divide\Trueepihead by \SCALE}
\newcount\MonoTail%
\global\MonoTail=\headsize%
\global\multiply\MonoTail by 6324%
\global\divide\MonoTail by 10000%
\newcount\EpiHead%
\global\EpiHead=\epihead%
\global\multiply\EpiHead by 8944%
\global\divide\EpiHead by 10000%
\newcount\TrueMonoTail%
\newcount\TrueEpiHead%
\def\TrueTail{\TrueMonoTail=\MonoTail%
\multiply\TrueMonoTail by 100%
\divide\TrueMonoTail by \SCALE}%
\def\TrueHead{\TrueEpiHead=\EpiHead%
\multiply\TrueEpiHead by 100%
\divide\TrueEpiHead by \SCALE}
\newcount\monotaiL%
\global\monotaiL=\headsize%
\global\multiply\monotaiL by 3162%
\global\divide\monotaiL by 10000%
\newcount\epiheaD%
\global\epiheaD=\epihead%
\global\multiply\epiheaD by 4472%
\global\divide\epiheaD by 10000%
\newcount\truemonotaiL%
\newcount\trueepiheaD%
\def\truetaiL{\truemonotaiL=\monotaiL%
\multiply\truemonotaiL by 100%
\divide\truemonotaiL by \SCALE}%
\def\trueheaD{\trueepiheaD=\epiheaD%
\multiply\trueepiheaD by 100%
\divide\trueepiheaD by \SCALE}
% INITIALIZATION
\newcount\SCALE%
\newcount\NUMBER%
\newcount\LINE%
\newcount\COLUMN%
\newcount\WIDTH%
\newcount\SOURCE%
\newcount\ARROW%
\newcount\TARGET%
\newcount\ARROWLENGTH%
\newcount\NUMBEROFDOTS%
\newcounter{x}%
\newcounter{y}%
\newcounter{z}%
\newcounter{horizontal}%
\newcounter{vertical}%
\newskip\itemlength%
\newskip\firstitem%
\newskip\seconditem%
\newcommand{\printarrow}{}%
\newcount\X%
\newcount\Y%
\newcount\Z%
% MACROS FOR DESIGNING DIAGRAMS
% \truex{n} divides n x 100 by the scaling factor and puts the result
% in counter x
\newcommand{\truex}[1]{%
\NUMBER=#1%
\multiply\NUMBER by 100%
\divide\NUMBER by \SCALE%
\setcounter{x}{\NUMBER}}%
% \truey{n} divides n x 100 by the scaling factor and puts the result
% in counter y
\newcommand{\truey}[1]{%
\NUMBER=#1%
\multiply\NUMBER by 100%
\divide\NUMBER by \SCALE%
\setcounter{y}{\NUMBER}}%
% \truez{n} divides n x 100 by the scaling factor and puts the result
% in counter z
\newcommand{\truez}[1]{%
\NUMBER=#1%
\multiply\NUMBER by 100%
\divide\NUMBER by \SCALE%
\setcounter{z}{\NUMBER}}%
% \changecounters computes the values of the various parameters required
% to design an arrow with adjusted length.
\newcommand{\changecounters}[1]{%
\SOURCE=\ARROW%
\ARROW=\TARGET%
\settowidth{\itemlength}{#1}%
\ifdim \itemlength > 2800\unitlength%
\addtolength{\itemlength}{-2800\unitlength}%
\TARGET=\itemlength%
\divide\TARGET by 1310%
\multiply\TARGET by 100%
\divide\TARGET by \SCALE%
\else%
\TARGET=0%
\fi%
\ARROWLENGTH=5000%
\advance\ARROWLENGTH by -\SOURCE%
\advance\ARROWLENGTH by -\TARGET%
\divide\ARROWLENGTH by 100%
\advance\SOURCE by -\TARGET}%
% \initialize initializes the counters required to produce the diagram
% and defines the formal dimensions of the diagram to be (0,0).
\newcommand{\initialize}[1]{%
\LINE=0%
\COLUMN=0%
\WIDTH=0%
\ARROW=0%
\TARGET=0%
\changecounters{#1}%
\renewcommand{\printarrow}{#1}%
\begin{center}%
\vspace{2pt}%
\begin{picture}(0,0)}%
% \DIAGV{n} starts the construction of a diagram scaled by a factor
% n percent, computes the scaled unit length and the unscaling factor.
\newcommand{\DIAGV}[2]{%
\checkmode%
\SCALE=#1%
\setlength{\unitlength}{655sp}%
\multiply\unitlength by \SCALE%
\divide\unitlength by 100%
\initialize{\mbox{$#2$}}}%
% \n introduces the next item of the diagram, computes its parameters
% and prints the previous item.
\newcommand{\n}[1]{%
\changecounters{\mbox{$#1$}}%
\put(\COLUMN,\LINE){\makebox(0,0){\printarrow}}%
\thinlines%
\renewcommand{\printarrow}{\mbox{$#1$}}%
\advance\COLUMN by 4000}%
% \nn prints the last item of a line and starts a new line.
\newcommand{\nn}[1]{%
\put(\COLUMN,\LINE){\makebox(0,0){\printarrow}}%
\thinlines%
\ifnum \WIDTH < \COLUMN%
\WIDTH=\COLUMN%
\else%
\fi%
\advance\LINE by -4000%
\COLUMN=0%
\ARROW=0%
\TARGET=0%
\changecounters{\mbox{$#1$}}%
\renewcommand{\printarrow}{\mbox{$#1$}}}%
% \conclude prints the last item of the diagram and sets the
% dimensions of the diagram;
\newcommand{\conclude}{%
\put(\COLUMN,\LINE){\makebox(0,0){\printarrow}}%
\thinlines%
\ifnum \WIDTH < \COLUMN%
\WIDTH=\COLUMN%
\else%
\fi%
\setcounter{horizontal}{\WIDTH}%
\setcounter{vertical}{-\LINE}%
\end{picture}}%
% \diag prints the last item of the diagram and takes care of the spacing
\newcommand{\diag}{%
\conclude%
\raisebox{0pt}[0pt][\value{vertical}\unitlength]{}%
\hspace*{\value{horizontal}\unitlength}%
\vspace{12pt}%
\end{center}%
\setlength{\unitlength}{1pt}%
\global\diagramfalse}%
% \diagv{t}{l}{b} prints the last item of the diagram and
% adds a t points extra space at the top of the diagram
% adds a l points extra space at the left of the diagram
% adds a b points extra space at the bottom of the diagram
\newcommand{\diagv}[3]{%
\conclude%
\NUMBER=#1%
\rule{0pt}{\NUMBER pt}%
\hspace*{-#2pt}%
\raisebox{0pt}[0pt][\value{vertical}\unitlength]{}%
\hspace*{\value{horizontal}\unitlength}%6
\NUMBER=#3%
\advance\NUMBER by 12%
\vspace*{\NUMBER pt}%
\end{center}%
\setlength{\unitlength}{1pt}%
\global\diagramfalse}%
% \movename(n,m){f} moves the name f of the arrow n points right
% and m points up.
\def\movename(#1,#2)#3{%
\hspace{#1pt}%
\raisebox{#2pt}[5pt][2pt]{\raisebox{#2pt}{$#3$}}%
\hspace{-#1pt}}%
% \movearrow(n,m){\...} moves arrow \... n points right
% and m points up.
\def\movearrow(#1,#2)#3{%
\makebox[0pt]{%
\hspace{#1pt}\hspace{#1pt}%
\raisebox{#2pt}[0pt][0pt]{\raisebox{#2pt}{$#3$}}}}%
% \movevertex(n,m){A} moves vertex A n points right and m points up
\def\movevertex(#1,#2)#3{%
\mbox{\hspace{#1pt}%
\raisebox{#2pt}{\raisebox{#2pt}{$#3$}}%
\hspace{-#1pt}}}%
% \movevertexleft{XXX} moves vertex XXX left
\newcommand{\movevertexleft}[1]{\makebox[2800\unitlength][r]{$#1$}}
% \movevertexright{XXX} moves vertex XXX right
\newcommand{\movevertexright}[1]{\makebox[2800\unitlength][l]{$#1$}}
% \crosslength{P}{Q} computes the formal dimensions of the
% superposition of pictures P and Q
\newcommand{\crosslength}[2]{%
\settowidth{\firstitem}{#1}%
\settowidth{\seconditem}{#2}%
\ifdim\firstitem < \seconditem%
\itemlength=\seconditem%
\else%
\itemlength=\firstitem%
\fi%
\divide\itemlength by 2%
\hspace{\itemlength}}%
% \cross{P}{Q} superposes pictures P and Q
\newcommand{\cross}[2]{%
\crosslength{\mbox{$#1$}}{\mbox{$#2$}}%
\begin{picture}(0,0)%
\put(0,0){\makebox(0,0){$#1$}}%
\thinlines%
\put(0,0){\makebox(0,0){$#2$}}%
\thinlines%
\end{picture}%
\crosslength{\mbox{$#1$}}{\mbox{$#2$}}}%
% \bold prints the next arrow in bold-face type
\newcommand{\bold}{\ifdiagram\thicklines\else\typeout{Sorry: command
\string\bold does not apply to text arrows; I am ignoring it.}\fi}
% \unbold switches back to normal arrows
\newcommand{\unbold}{\thinlines}
% SHORTENING THE TYPING OF DIAGRAMS
\def\basicDIAG#1¤{\DIAGV{\defaultscale}{#1}\@ifnexttok¤{\finishline}{\basicn}}
\def\basicDIAGV[#1]#2¤{\DIAGV{#1}{#2}\@ifnexttok¤{\finishline}{\basicn}}
\def\basicn#1¤{\n{#1}\@ifnexttok¤{\finishline}{\basicn}}
\def\basicnn#1¤{\nn{#1}\@ifnexttok¤{\finishline}{\basicn}}
\def\finishline#1{\@ifnextchar\end{\diag}%
{\@ifnextchar\spacing{\relax}{\basicnn}}}
\def\spacing(#1,#2,#3){\diagv{#1}{#2}{#3}}
\newif\ifcaption%
\newenvironment{diagram}{%
\iffloatdiag\relax\else
\global\def\diagramcaption##1{%
\global\captiontrue%
\global\def\@diagcaption{##1}}%
\global\def\@diagcaption{}\fi%
\@ifnextchar[{\basicDIAGV}{\basicDIAG}}%
{\iffloatdiag\relax\else%
\ifcaption
\begin{center}\mbox{}\@diagcaption\end{center}%
\else\relax\fi\fi\global\captionfalse}
\global\captionfalse
% MACROS FOR FLOATING DIAGRAMS
\gdef\@diaglabel{Diagram}
\gdef\diagramlabel#1{\gdef\@diaglabel{#1}}
\newcounter{Diagram}
\setcounter{Diagram}{0}
\def\theDiagram{\@arabic\c@Diagram}
\def\fps@Diagram{tbp}
\def\ftype@Diagram{1}
\def\ext@Diagram{lof}
\def\fnum@Diagram{\@diaglabel\ \theDiagram}
\def\Diagram{\@float{Diagram}}
\let\endDiagram\end@float
\@namedef{Diagram*}{\@dblfloat{Diagram}}
\@namedef{endDiagram*}{\end@dblfloat}
\def\setdiagramcounter#1{\@addtoreset{Diagram}{#1}%
\def\theDiagram{\arabic{#1}.\@arabic\c@Diagram}}
\newif\iffloatdiag
\newenvironment{floatingdiagram}{%
\global\floatdiagtrue%
\long\def\@makecaption##1##2{
\vskip 0pt
\setbox\@tempboxa\hbox{##1##2}
\ifdim \wd\@tempboxa >\hsize \unhbox\@tempboxa\par \else \hbox
to\hsize{\hfil\box\@tempboxa\hfil}
\fi}%
\global\def\diagramcaption##1{\global\def\@diagcaption{: ##1}}%
\global\def\@diagcaption{}%
\begin{Diagram}[tbp]\begin{diagram}}%
{\end{diagram}\caption{\@diagcaption}\end{Diagram}%
\global\floatdiagfalse}
\global\floatdiagfalse
% MACROS FOR DRAWING TEXT PICTURES
% moving a name up
\newcommand{\TUP}[1]{\raisebox{0pt}[0pt][3pt]{}#1}
% moving a name down
\newcommand{\TDOWN}[1]{\raisebox{0pt}[6pt][0pt]{}#1}
% \tlowername{P}{f} puts the name f under the picture P
\newcommand{\tlowername}[2]%
{$\stackrel{\makebox[1pt]{#1}}%
{\begin{picture}(0,0)%
\put(0,0){\makebox(0,6)[t]{\makebox[1pt]{$\scriptstyle#2$}}}%
\end{picture}}$}%
% \tcase{P} draws the picture P with length \textarrowlength pt.
\newcommand{\tcase}[1]{%
\testtextmode%
\setlength{\unitlength}{0.01pt}%
\makebox[\actualtextarrowspace pt]%
{\raisebox{2.5pt}{#1{\actualtextarrowlength}}}%
\setlength{\unitlength}{1pt}}%
% \Tcase{P}{f} draws the picture P with upper name f
% and length \textarrowlength pt.
\newcommand{\Tcase}[2]{%
\testtextmode%
\setlength{\unitlength}{0.01pt}%
\makebox[\actualtextarrowspace pt]%
{\raisebox{2.5pt}{$\stackrel{\scriptstyle #2}{#1{\actualtextarrowlength}}$}}%
\setlength{\unitlength}{1pt}}%
% \tbicase{P} draws the bi-picture P
% with length \textarrowlength pt.
\newcommand{\tbicase}[1]{%
\testtextmode%
\setlength{\unitlength}{0.01pt}%
\makebox[\actualtextarrowspace pt]%
{\raisebox{1pt}{#1{\actualtextarrowlength}}}%
\setlength{\unitlength}{1pt}}%
% \Tbicase{P}{f}{g} draws the bi-picture P with names f, g
% and length \textarrowlength pt.
\newcommand{\Tbicase}[3]{%
\testtextmode%
\setlength{\unitlength}{0.01pt}%
\makebox[\actualtextarrowspace pt]%
{\raisebox{-1pt}%
{$\stackrel{\scriptstyle #2}%
{\mbox{\tlowername{#1{\actualtextarrowlength}}%
{\scriptstyle #3}}}$}}%
\setlength{\unitlength}{1pt}}%
% MACROS FOR DRAWING DISPLAYED PICTURES
% moving a name up
\newcommand{\DUP}[1]{\raisebox{0pt}[0pt][4pt]{}#1}
% moving a name down
\newcommand{\DDOWN}[1]{\raisebox{0pt}[9pt][0pt]{}#1}
% \dlowername{P}{f} puts the name f under the picture P
\newcommand{\dlowername}[2]%
{$\stackrel{\makebox[1pt]{#1}}%
{\begin{picture}(0,0)%
\put(0,0){\makebox(0,6)[t]{\makebox[1pt]{$\textstyle#2$}}}%
\end{picture}}$}%
% \dcase{P} draws the picture P with length \displayarrowlength pt.
\newcommand{\dcase}[1]{%
\testtextmode%
\setlength{\unitlength}{0.01pt}%
\makebox[\actualdisplayarrowspace pt]%
{\raisebox{2.5pt}{#1{\actualdisplayarrowlength}}}%
\setlength{\unitlength}{1pt}}%
% \Dcase{P}{f} draws the picture P with upper name f
% and length \displayarrowlength pt.
\newcommand{\Dcase}[2]{%
\testtextmode%
\setlength{\unitlength}{0.01pt}%
\makebox[\actualdisplayarrowspace pt]%
{\raisebox{2.5pt}{$\stackrel{\textstyle #2}{#1{\actualdisplayarrowlength}}$}}%
\setlength{\unitlength}{1pt}}%
% \dbicase{P} draws the bi-picture P
% with length \displayarrowlength pt.
\newcommand{\dbicase}[1]{%
\testtextmode%
\setlength{\unitlength}{0.01pt}%
\makebox[\actualdisplayarrowspace pt]%
{\raisebox{1pt}{#1{\actualdisplayarrowlength}}}%
\setlength{\unitlength}{1pt}}%
% \Dbicase{P}{f}{g} draws the bi-picture P with names f, g
% and length \displayarrowlength pt.
\newcommand{\Dbicase}[3]{%
\testtextmode%
\setlength{\unitlength}{0.01pt}%
\makebox[\actualdisplayarrowspace pt]%
{\raisebox{-1pt}%
{$\stackrel{\textstyle #2}%
{\mbox{\tlowername{#1{\actualdisplayarrowlength}}%
{\textstyle #3}}}$}}%
\setlength{\unitlength}{1pt}}%
% IN-TEXT ARROWS
% \AR{n} draws an arrow of length n units
\newcommand{\AR}[1]%
{\begin{picture}(#1,0)%
\put(0,0){\line(1,0){#1}}%
\put(#1,0){\ehead}%
\end{picture}}%
% \DIST{n} draws a distributor of length n units
\newcommand{\DIST}[1]%
{\begin{picture}(#1,0)%
\put(0,0){\line(1,0){#1}}%
\put(#1,0){\ehead}%
\NUMBER=#1%
\divide\NUMBER by 2%
\put(\NUMBER,0){\circle{400}}%
\end{picture}}%
% \DOTAR{n} draws a dotted arrow of length n units
\newcommand{\DOTAR}[1]%
{\NUMBEROFDOTS=#1%
\divide\NUMBEROFDOTS by 300%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(#1,0)%
\multiput(0,0)(300,0){\NUMBEROFDOTS}{\circle*{100}}%
\put(#1,0){\ehead}%
\end{picture}}%
% \MONO{n} draws a monomorphism of length n units
\newcommand{\MONO}[1]%
{\monolength=#1%
\advance\monolength by -\monotail%
\begin{picture}(#1,0)%
\put(\monotail,0){\line(1,0){\monolength}}%
\put(#1,0){\ehead}%
\put(\monotail,0){\ehead}%
\end{picture}}%
% \EPI{n} draws an epimorphism of length n units
\newcommand{\EPI}[1]%
{\epilength=#1%
\advance\epilength by -\epihead%
\begin{picture}(#1,0)(-#1,0)%
\put(-#1,0){\line(1,0){\epilength}}%
\put(-\epihead,0){\ehead}%
\put(0,0){\ehead}%
\end{picture}}%
% \BIMO{n} draws a bimorphism of length n units
\newcommand{\BIMO}[1]%
{\monolength=#1%
\advance\monolength by -\monotail%
\epilength=\monolength%
\advance\epilength by -\epihead%
\begin{picture}(#1,0)(-#1,0)%
\put(-\monolength,0){\line(1,0){\epilength}}%
\put(-\monolength,0){\ehead}%
\put(-\epihead,0){\ehead}%
\put(0,0){\ehead}%
\end{picture}}%
% \BIAR{n} draws a pair of arrows of length n units
\newcommand{\BIAR}[1]%
{\begin{picture}(#1,700)%
\put(0,0){\line(1,0){#1}}%
\put(#1,0){\ehead}%
\put(0,700){\line(1,0){#1}}%
\put(#1,700){\ehead}%
\end{picture}}%
% \BIDIST{n} draws a pair of distributors of length n units
\newcommand{\BIDIST}[1]%
{\begin{picture}(#1,700)%
\put(0,0){\line(1,0){#1}}%
\put(#1,0){\ehead}%
\put(0,700){\line(1,0){#1}}%
\put(#1,700){\ehead}%
\NUMBER=#1%
\divide\NUMBER by 2%
\put(\NUMBER,0){\circle{400}}%
\put(\NUMBER,700){\circle{400}}%
\end{picture}}%
% \EQL{n} draws an equality of length n units
\newcommand{\EQL}[1]%
{\begin{picture}(#1,0)%
\put(0,100){\line(1,0){#1}}%
\put(0,-100){\line(1,0){#1}}%
\end{picture}}%
% \ADJAR{n} draws a pair of adjoint arrows of length n units
\newcommand{\ADJAR}[1]%
{\begin{picture}(#1,700)%
\put(0,0){\line(1,0){#1}}%
\put(#1,0){\ehead}%
\put(#1,700){\line(-1,0){#1}}%
\put(0,700){\whead}
\end{picture}}%
% \ADJDIST{n} draws a pair of adjoint distibutors of length n units
\newcommand{\ADJDIST}[1]%
{\begin{picture}(#1,700)%
\put(0,0){\line(1,0){#1}}%
\put(#1,0){\ehead}%
\put(#1,700){\line(-1,0){#1}}%
\put(0,700){\whead}
\NUMBER=#1%
\divide\NUMBER by 2%
\put(\NUMBER,0){\circle{400}}%
\put(\NUMBER,700){\circle{400}}%
\end{picture}}%
% All the following commands produce arrows with length 20pt
% and scriptstyle names in math mode but arrows with length
% \displayarrowlength pt and textstyle names in display math mode.
% arrow
\newcommand{\ar}{\ifinner\tcase{\AR}\else\dcase{\AR}\fi}%
% arrow with upper name [1]
\newcommand{\Ar}[1]{\ifinner\Tcase{\AR}{#1}\else\Dcase{\AR}{#1}\fi}%
% distributor
\newcommand{\dist}{\ifinner\tcase{\DIST}\else\dcase{\DIST}\fi}%
% distributor with upper name [1]
\newcommand{\Dist}[1]{\ifinner\Tcase{\DIST}{\TUP{#1}}%
\else\Dcase{\DIST}{\TUP{#1}}\fi}%
% dotted arrow
\newcommand{\dotar}{\ifinner\tcase{\DOTAR}\else\dcase{\DOTAR}\fi}%
% dotted arrow with upper name [1]
\newcommand{\Dotar}[1]{\ifinner\Tcase{\DOTAR}{#1}%
\else\Dcase{\DOTAR}{#1}\fi}%
% monomorphism
\newcommand{\mono}{\ifinner\tcase{\MONO}\else\dcase{\MONO}\fi}%
% monomorphism with upper name [1]
\newcommand{\Mono}[1]{\ifinner\Tcase{\MONO}{#1}\else\Dcase{\MONO}{#1}\fi}%
% epimorphism
\newcommand{\epi}{\ifinner\tcase{\EPI}\else\dcase{\EPI}\fi}%
% epimorphism with upper name [1]
\newcommand{\Epi}[1]{\ifinner\Tcase{\EPI}{#1}\else\Dcase{\EPI}{#1}\fi}%
% bimorphism
\newcommand{\bimo}{\ifinner\tcase{\BIMO}\else\dcase{\BIMO}\fi}%
% bimorphism with upper name [1]
\newcommand{\Bimo}[1]{\ifinner\Tcase{\BIMO}{#1}%
\else\Dcase{\BIMO}{#1}\fi}%
% isomorphism
\newcommand{\iso}{\ifinner\Tcase{\AR}{\cong}\else\Dcase{\AR}{\cong}\fi}%
% isomorphism with upper name [1]
\newcommand{\Iso}[1]{\ifinner\Tcase{\AR}{\cong{#1}}%
\else\Dcase{\AR}{\cong{#1}}\fi}%
% pair of arrows
\newcommand{\biar}{\ifinner\tbicase{\BIAR}\else\dbicase{\BIAR}\fi}%
% pair of arrows with names [1],[2]
\newcommand{\Biar}[2]{\ifinner\Tbicase{\BIAR}{#1}{#2}%
\else\Dbicase{\BIAR}{#1}{#2}\fi}%
% pair of distributors
\newcommand{\bidist}{\ifinner\tbicase{\BIDIST}\else\dbicase{\BIDIST}\fi}%
% pair of distributors with names [1],[2]
\newcommand{\Bidist}[2]{\ifinner\Tbicase{\BIDIST}{\TUP{#1}}{\TDOWN{#2}}%
\else\Dbicase{\BIDIST}{\DUP{#1}}{\DDOWN{#2}}\fi}%
% equality
\newcommand{\eql}{\ifinner\tcase{\EQL}\else\dcase{\EQL}\fi}%
% equality with name [1]
\newcommand{\Eql}[1]{\ifinner\Tcase{\EQL}{\TUP{#1}}%
\else\Dcase{\EQL}{\DUP{#1}}\fi}%
% pair of adjoint arrows
\newcommand{\adjar}{\ifinner\tbicase{\ADJAR}\else\dbicase{\ADJAR}\fi}%
% pair of adjoint arrows with names [1],[2]
\newcommand{\Adjar}[2]{\ifinner\Tbicase{\ADJAR}{#1}{#2}%
\else\Dbicase{\ADJAR}{#1}{#2}\fi}%
% pair of adjoint distributors
\newcommand{\adjdist}{\ifinner\tbicase{\ADJDIST}\else\dbicase{\ADJDIST}\fi}%
% pair of adjoint distributors with names [1],[2]
\newcommand{\Adjdist}[2]{\ifinner\Tbicase{\ADJDIST}{\TUP{#1}}{\TDOWN{#2}}%
\else\Dbicase{\ADJDIST}{\DUP{#1}}{\DDOWN{#2}}\fi}%
% IN-TEXT BACK ARROWS
% \BKAR{n} draws a pointing back arrow of length n units
\newcommand{\BKAR}[1]%
{\begin{picture}(#1,0)%
\put(#1,0){\line(-1,0){#1}}%
\put(0,0){\whead}%
\end{picture}}%
% \BKDIST{n} draws a pointing back distributor of length n units
\newcommand{\BKDIST}[1]%
{\begin{picture}(#1,0)%
\put(#1,0){\line(-1,0){#1}}%
\put(0,0){\whead}%
\NUMBER=#1%
\divide\NUMBER by 2%
\put(\NUMBER,0){\circle{400}}%
\end{picture}}%
% \BKDOTAR{n} draws a backward dotted arrow
% of length n units
\newcommand{\BKDOTAR}[1]%
{\NUMBEROFDOTS=#1%
\divide\NUMBEROFDOTS by 300%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(#1,0)%
\multiput(#1,0)(-300,0){\NUMBEROFDOTS}{\circle*{100}}%
\put(0,0){\whead}%
\end{picture}}%
% \BKMONO{n} draws a pointing back monomorphism of length n units
\newcommand{\BKMONO}[1]%
{\monolength=#1%
\advance\monolength by -\monotail%
\begin{picture}(#1,0)(-#1,0)%
\put(-\monotail,0){\line(-1,0){\monolength}}%
\put(-\monotail,0){\whead}%
\put(-#1,0){\whead}%
\end{picture}}%
% \BKEPI{n} draws a pointing back epimorphism of length n units
\newcommand{\BKEPI}[1]%
{\epilength=#1%
\advance\epilength by -\epihead%
\begin{picture}(#1,0)%
\put(#1,0){\line(-1,0){\epilength}}%
\put(\epihead,0){\whead}%
\put(0,0){\whead}%
\end{picture}}%
% \BKBIMO{n} draws a pointing back bimorphism of length n units
\newcommand{\BKBIMO}[1]%
{\monolength=#1%
\advance\monolength by -\monotail%
\epilength=\monolength%
\advance\epilength by -\epihead%
\begin{picture}(#1,0)%
\put(\monolength,0){\line(-1,0){\epilength}}%
\put(\monolength,0){\whead}%
\put(\epihead,0){\whead}%
\put(0,0){\whead}%
\end{picture}}%
% \BKBIAR{n} draws a pair of pointing back arrows of length n units
\newcommand{\BKBIAR}[1]%
{\begin{picture}(#1,700)%
\put(#1,0){\line(-1,0){#1}}%
\put(0,0){\whead}%
\put(#1,700){\line(-1,0){#1}}%
\put(0,700){\whead}%
\end{picture}}%
% \BKBIDIST{n} draws a pair of pointing back distributors of length n units
\newcommand{\BKBIDIST}[1]%
{\begin{picture}(#1,700)%
\put(#1,0){\line(-1,0){#1}}%
\put(0,0){\whead}%
\put(#1,700){\line(-1,0){#1}}%
\put(0,700){\whead}%
\NUMBER=#1%
\divide\NUMBER by 2%
\put(\NUMBER,0){\circle{400}}%
\put(\NUMBER,700){\circle{400}}%
\end{picture}}%
% \BKADJAR{n} draws a pair of adjoint arrows of length n units
\newcommand{\BKADJAR}[1]%
{\begin{picture}(#1,700)%
\put(0,700){\line(1,0){#1}}%
\put(#1,700){\ehead}%
\put(#1,0){\line(-1,0){#1}}%
\put(0,0){\whead}%
\end{picture}}%
% \BKADJDIST{n} draws a pair of adjoint distributors of length n units
\newcommand{\BKADJDIST}[1]%
{\begin{picture}(#1,700)%
\put(0,700){\line(1,0){#1}}%
\put(#1,700){\ehead}%
\put(#1,0){\line(-1,0){#1}}%
\put(0,0){\whead}%
\NUMBER=#1%
\divide\NUMBER by 2%
\put(\NUMBER,0){\circle{400}}%
\put(\NUMBER,700){\circle{400}}%
\end{picture}}%
% All the following commands produce back arrows with length 20pt
% and scriptstyle names in math mode but arrows with length
% \displayarrowlength and textstyle names in display math mode.
% back arrow
\newcommand{\bkar}{\ifinner\tcase{\BKAR}\else\dcase{\BKAR}\fi}%
% back arrow with upper name [1]
\newcommand{\Bkar}[1]{\ifinner\Tcase{\BKAR}{#1}\else\Dcase{\BKAR}{#1}\fi}%
% back distributor
\newcommand{\bkdist}{\ifinner\tcase{\BKDIST}\else\dcase{\BKDIST}\fi}%
% back distributor with upper name [1]
\newcommand{\Bkdist}[1]{\ifinner\Tcase{\BKDIST}{\TUP{#1}}%
\else\Dcase{\BKDIST}{\TUP{#1}}\fi}%
% backward dotted arrow
\newcommand{\bkdotar}{\ifinner\tcase{\BKDOTAR}\else\dcase{\BKDOTAR}\fi}%
% backward dotted arrow with upper name [1]
\newcommand{\Bkdotar}[1]{\ifinner\Tcase{\BKDOTAR}{#1}%
\else\Dcase{\BKDOTAR}{#1}\fi}%
% back monomorphism
\newcommand{\bkmono}{\ifinner\tcase{\BKMONO}\else\dcase{\BKMONO}\fi}%
% back monomorphism with upper name [1]
\newcommand{\Bkmono}[1]{\ifinner\Tcase{\BKMONO}{#1}%
\else\Dcase{\BKMONO}{#1}\fi}%
% back epimorphism
\newcommand{\bkepi}{\ifinner\tcase{\BKEPI}\else\dcase{\BKEPI}\fi}%
% back epimorphism with upper name [1]
\newcommand{\Bkepi}[1]{\ifinner\Tcase{\BKEPI}{#1}%
\else\Dcase{\BKEPI}{#1}\fi}%
% back bimorphism
\newcommand{\bkbimo}{\ifinner\tcase{\BKBIMO}\else\dcase{\BKBIMO}\fi}%
% back bimorphism with upper name [1]
\newcommand{\Bkbimo}[1]{\ifinner\Tcase{\BKBIMO}{\hspace{9pt}#1}%
\else\Dcase{\BKBIMO}{\hspace{9pt}#1}\fi}%
% back isomorphism
\newcommand{\bkiso}{\ifinner\Tcase{\BKAR}{\cong}%
\else\Dcase{\BKAR}{\cong}\fi}%
% back isomorphism with upper name [1]
\newcommand{\Bkiso}[1]{\ifinner\Tcase{\BKAR}{\cong{#1}}%
\else\Dcase{\BKAR}{\cong{#1}}\fi}%
% pair of back arrows
\newcommand{\bkbiar}{\ifinner\tbicase{\BKBIAR}\else\dbicase{\BKBIAR}\fi}%
% pair of back arrows with names [1],[2]
\newcommand{\Bkbiar}[2]{\ifinner\Tbicase{\BKBIAR}{#1}{#2}%
\else\Dbicase{\BKBIAR}{#1}{#2}\fi}%
% pair of back distributors
\newcommand{\bkbidist}{\ifinner\tbicase{\BKBIDIST}%
\else\dbicase{\BKBIDIST}\fi}%
% pair of back distributors with names [1],[2]
\newcommand{\Bkbidist}[2]{\ifinner\Tbicase{\BKBIDIST}{\TUP{#1}}{\TDOWN{#2}}%
\else\Tbicase{\BKBIDIST}{\DUP{#1}}{\DDOWN{#2}}\fi}%
% back equality
\let\bkeql=\eql%
% back equality with name [1]
\let\Bkeql=\Eql%
% back pair of adjoint arrows
\newcommand{\bkadjar}{\ifinner\tbicase{\BKADJAR}%
\else\dbicase{\BKADJAR}\fi}%
% back pair of adjoint arrows with names [1],[2]
\newcommand{\Bkadjar}[2]{\ifinner\Tbicase{\BKADJAR}{#1}{#2}%
\else\Dbicase{\BKADJAR}{#1}{#2}\fi}%
% back pair of adjoint distributors
\newcommand{\bkadjdist}{\ifinner\tbicase{\BKADJDIST}%
\else\dbicase{\BKADJDIST}\fi}%
% back pair of adjoint distributors with names [1],[2]
\newcommand{\Bkadjdist}[2]{\ifinner\Tbicase{\BKADJDIST}{\TUP{#1}}{\TDOWN{#2}}%
\else\Dbicase{\BKADJDIST}{\TUP{#1}}{\TDOWN{#2}}\fi}%
% MACROS FOR DRAWING HORIZONTAL PICTURES
% \lowername{P}{f} puts the name f under the picture P
\newcommand{\lowername}[2]%
{$\stackrel{\makebox[1pt]{#1}}%
{\begin{picture}(0,0)%
\truex{600}%
\put(0,0){\makebox(0,\value{x})[t]{\makebox[1pt]{$#2$}}}%
\end{picture}}$}%
% \hcase{P}{n} draws the picture P with length n units
\newcommand{\hcase}[2]%
{\testdiagrammode\makebox[0pt]%
{\raisebox{0pt}[0pt][0pt]{#1{#2}}}}%
% \Hcase{P}{f}{n} draws the picture P with upper name f
% and length n units.
\newcommand{\Hcase}[3]%
{\testdiagrammode\makebox[0pt]
{\raisebox{0pt}[0pt][0pt]%
{$\stackrel{\makebox[0pt]{$\textstyle{#2}$}}{#1{#3}}$}}}%
% \hcasE{P}{f}{n} draws the picture P with lower name f
% and length n units.
\newcommand{\hcasE}[3]%
{\testdiagrammode\makebox[0pt]%
{\raisebox{-8pt}[0pt][0pt]%
{\lowername{#1{#3}}{#2}}}}%
% \Hisocase{P}{f}{g}{n} draws an arrow P with names f, g
% and length n units.
\newcommand{\Hisocase}[4]%
{\testdiagrammode\makebox[0pt]
{\raisebox{-8pt}[0pt][0pt]%
{$\stackrel{\makebox[0pt]{$\textstyle{#2}$}}%
{\mbox{\lowername{#1{#4}}{#3}}}$}}}%
% \hbicase{P}{n} draws the bi-picture P with length n units.
\newcommand{\hbicase}[2]%
{\testdiagrammode\makebox[0pt]%
{\raisebox{-2.4pt}[0pt][0pt]{#1{#2}}}}%
% \Hbicase{P}{f}{g}{n} draws the bi-picture P with names f, g
% and length n units.
\newcommand{\Hbicase}[4]%
{\testdiagrammode\makebox[0pt]
{\raisebox{-10.4pt}[0pt][0pt]%
{$\stackrel{\makebox[0pt]{$\textstyle{#2}$}}%
{\mbox{\lowername{#1{#4}}{#3}}}$}}}%
% EAST ARROWS
% \EAR{n} draws an east arrow of length n units
\newcommand{\EAR}[1]%
{\begin{picture}(#1,0)%
\put(0,0){\line(1,0){#1}}%
\put(#1,0){\ehead}%
\end{picture}}%
% \EDIST{n} draws an east distributor of length n units
\newcommand{\EDIST}[1]%
{\begin{picture}(#1,0)%
\put(0,0){\line(1,0){#1}}%
\put(#1,0){\ehead}%
\truex{400}
\NUMBER=#1%
\divide\NUMBER by 2%
\put(\NUMBER,0){\circle{\value{x}}}
\end{picture}}%
% \EDOTAR draws a dotted arrow of length n units
\newcommand{\EDOTAR}[1]%
{\truex{100}\truey{300}%
\NUMBEROFDOTS=#1%
\divide\NUMBEROFDOTS by \value{y}%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(#1,0)%
\multiput(0,0)(\value{y},0){\NUMBEROFDOTS}%
{\circle*{\value{x}}}%
\put(#1,0){\ehead}%
\end{picture}}%
% \EMONO{n} draws an east monomorphism of length n units
\newcommand{\EMONO}[1]%
{\truetail
\monolength=#1%
\advance\monolength by -\truemonotail%
\begin{picture}(#1,0)%
\put(\truemonotail,0){\line(1,0){\monolength}}%
\put(#1,0){\ehead}%
\put(\truemonotail,0){\ehead}%
\end{picture}}%
% \EEPI{n} draws an east epimorphism of length n units
\newcommand{\EEPI}[1]%
{\truehead%
\epilength=#1%
\advance\epilength by -\trueepihead%
\begin{picture}(#1,0)(-#1,0)%
\put(-#1,0){\line(1,0){\epilength}}%
\put(-\trueepihead,0){\ehead}%
\put(0,0){\ehead}%
\end{picture}}%
% \EBIMO{n} draws an east bimorphism of length n units
\newcommand{\EBIMO}[1]%
{\truehead\truetail%
\monolength=#1%
\advance\monolength by -\truemonotail%
\epilength=\monolength%
\advance\epilength by -\trueepihead%
\begin{picture}(#1,0)(-#1,0)%
\put(-\monolength,0){\line(1,0){\epilength}}%
\put(-\monolength,0){\ehead}%
\put(-\trueepihead,0){\ehead}%
\put(0,0){\ehead}%
\end{picture}}%
% \EBIAR{n} draws an east pair of arrows of length n units
\newcommand{\EBIAR}[1]%
{\truex{700}%
\begin{picture}(#1,\value{x})%
\put(0,0){\line(1,0){#1}}%
\put(#1,0){\ehead}%
\put(0,\value{x}){\line(1,0){#1}}%
\put(#1,\value{x}){\ehead}%
\end{picture}}%
% \EBIDIST{n} draws an east pair of distributors of length n units
\newcommand{\EBIDIST}[1]%
{\truex{700}%
\begin{picture}(#1,\value{x})%
\put(0,0){\line(1,0){#1}}%
\put(#1,0){\ehead}%
\put(0,\value{x}){\line(1,0){#1}}%
\put(#1,\value{x}){\ehead}%
\truey{400}%
\NUMBER=#1%
\divide\NUMBER by 2%
\put(\NUMBER,0){\circle{\value{y}}}
\put(\NUMBER,\value{x}){\circle{\value{y}}}%
\end{picture}}%
% \EEQL{n} draws an east equality of length n units
\newcommand{\EEQL}[1]%
{\begin{picture}(#1,0)%
\truex{200}%
\put(0,\value{x}){\line(1,0){#1}}%
\put(0,0){\line(1,0){#1}}%
\end{picture}}%
% \EADJAR{n} draws an east pair of adjoint arrows of length n
% units
\newcommand{\EADJAR}[1]%
{\truex{700}%
\begin{picture}(#1,\value{x})%
\put(0,0){\line(1,0){#1}}%
\put(#1,0){\ehead}%
\put(#1,\value{x}){\line(-1,0){#1}}%
\put(0,\value{x}){\whead}%
\end{picture}}%
% \EADJDIST{n} draws an east pair of adjoint distributors of length n
% units
\newcommand{\EADJDIST}[1]%
{\truex{700}%
\begin{picture}(#1,\value{x})%
\put(0,0){\line(1,0){#1}}%
\put(#1,0){\ehead}%
\put(#1,\value{x}){\line(-1,0){#1}}%
\put(0,\value{x}){\whead}%
\truey{400}%
\NUMBER=#1%
\divide\NUMBER by 2%
\put(\NUMBER,0){\circle{\value{y}}}
\put(\NUMBER,\value{x}){\circle{\value{y}}}%
\end{picture}}%
% All the following commands produce east arrows
% basic east arrow
\def\basicear[#1]{%
\Z=#1%
\multiply \Z by 100%
\hcase{\EAR}{\Z}}%
% east arrow
\newcommand{\ear}{\@ifnextchar[{\basicear}%
{\hspace{\SOURCE\unitlength}\basicear[\ARROWLENGTH]}}%
% basic east arrow with upper name
\def\basicEar[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hcase{\EAR}{#2}{\Z}}%
% east arrow with upper name
\newcommand{\Ear}{\@ifnextchar[{\basicEar}%
{\hspace{\SOURCE\unitlength}\basicEar[\ARROWLENGTH]}}%
% basic east arrow with lower name
\def\basiceaR[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\hcasE{\EAR}{#2}{\Z}}%
% east arrow with lower name
\newcommand{\eaR}{\@ifnextchar[{\basiceaR}%
{\hspace{\SOURCE\unitlength}\basiceaR[\ARROWLENGTH]}}%
% basic east distributor
\def\basicedist[#1]{%
\Z=#1%
\multiply \Z by 100%
\hcase{\EDIST}{\Z}}%
% east distributor
\newcommand{\edist}{\@ifnextchar[{\basicedist}%
{\hspace{\SOURCE\unitlength}\basicedist[\ARROWLENGTH]}}%
% basic east distributor with upper name
\def\basicEdist[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hcase{\EDIST}{\DUP{#2}}{\Z}}%
% east distributor with upper name
\newcommand{\Edist}{\@ifnextchar[{\basicEdist}%
{\hspace{\SOURCE\unitlength}\basicEdist[\ARROWLENGTH]}}%
% basic east distributor with lower name
\def\basicedisT[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\hcasE{\EDIST}{\DDOWN{#2}}{\Z}}%
% east distributor with lower name
\newcommand{\edisT}{\@ifnextchar[{\basicedisT}%
{\hspace{\SOURCE\unitlength}\basicedisT[\ARROWLENGTH]}}%
% basic east dotted arrow
\def\basicedotar[#1]{%
\Z=#1%
\multiply \Z by 100%
\hcase{\EDOTAR}{\Z}}%
% east dotted arrow
\newcommand{\edotar}{\@ifnextchar[{\basicedotar}%
{\hspace{\SOURCE\unitlength}\basicedotar[\ARROWLENGTH]}}%
% basic east dotted arrow with upper name
\def\basicEdotar[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hcase{\EDOTAR}{#2}{\Z}}%
% east dotted arrow with upper name
\newcommand{\Edotar}{\@ifnextchar[{\basicEdotar}%
{\hspace{\SOURCE\unitlength}\basicEdotar[\ARROWLENGTH]}}%
% basic east dotted arrow with lower name
\def\basicedotaR[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\hcasE{\EDOTAR}{#2}{\Z}}%
% east dotted arrow with lower name
\newcommand{\edotaR}{\@ifnextchar[{\basicedotaR}%
{\hspace{\SOURCE\unitlength}\basicedotaR[\ARROWLENGTH]}}%
% basic east monomorphism
\def\basicemono[#1]{%
\Z=#1%
\multiply \Z by 100%
\hcase{\EMONO}{\Z}}%
% east arrow
\newcommand{\emono}{\@ifnextchar[{\basicemono}%
{\hspace{\SOURCE\unitlength}\basicemono[\ARROWLENGTH]}}%
% basic east monomorphism with upper name
\def\basicEmono[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hcase{\EMONO}{#2}{\Z}}%
% east monomorphism with upper name
\newcommand{\Emono}{\@ifnextchar[{\basicEmono}%
{\hspace{\SOURCE\unitlength}\basicEmono[\ARROWLENGTH]}}%
% basic east monomorphism with lower name
\def\basicemonO[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\hcasE{\EMONO}{#2}{\Z}}%
% east monomorphism with lower name
\newcommand{\emonO}{\@ifnextchar[{\basicemonO}%
{\hspace{\SOURCE\unitlength}\basicemonO[\ARROWLENGTH]}}%
% basic east epimorphism
\def\basiceepi[#1]{%
\Z=#1%
\multiply \Z by 100%
\hcase{\EEPI}{\Z}}%
% east epimorphism
\newcommand{\eepi}{\@ifnextchar[{\basiceepi}%
{\hspace{\SOURCE\unitlength}\basiceepi[\ARROWLENGTH]}}%
% basic east epimorphism with upper name
\def\basicEepi[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hcase{\EEPI}{#2}{\Z}}%
% east epimorphism with upper name
\newcommand{\Eepi}{\@ifnextchar[{\basicEepi}%
{\hspace{\SOURCE\unitlength}\basicEepi[\ARROWLENGTH]}}%
% basic east epimorphism with lower name
\def\basiceepI[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\hcasE{\EEPI}{#2}{\Z}}%
% east epimorphism with lower name
\newcommand{\eepI}{\@ifnextchar[{\basiceepI}%
{\hspace{\SOURCE\unitlength}\basiceepI[\ARROWLENGTH]}}%
% basic east bimorphism
\def\basicebimo[#1]{%
\Z=#1%
\multiply \Z by 100%
\hcase{\EBIMO}{\Z}}%
% east bimorphism
\newcommand{\ebimo}{\@ifnextchar[{\basicebimo}%
{\hspace{\SOURCE\unitlength}\basicebimo[\ARROWLENGTH]}}%
% basic east bimorphism with upper name
\def\basicEbimo[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hcase{\EBIMO}{#2}{\Z}}%
% east bimorphism with upper name
\newcommand{\Ebimo}{\@ifnextchar[{\basicEbimo}%
{\hspace{\SOURCE\unitlength}\basicEbimo[\ARROWLENGTH]}}%
% basic east bimorphism with lower name
\def\basicebimO[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\hcasE{\EBIMO}{#2}{\Z}}%
% east bimorphism with lower name
\newcommand{\ebimO}{\@ifnextchar[{\basicebimO}%
{\hspace{\SOURCE\unitlength}\basicebimO[\ARROWLENGTH]}}%
% basic east isomorphism
\def\basiceiso[#1]{%
\Z=#1%
\multiply \Z by 100%
\Hisocase{\EAR}{\cong}{}{\Z}}%
% east isomorphism
\newcommand{\eiso}{\@ifnextchar[{\basiceiso}%
{\hspace{\SOURCE\unitlength}\basiceiso[\ARROWLENGTH]}}%
% basic east isomorphism with upper name
\def\basicEiso[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hisocase{\EAR}{#2}{\cong}{\Z}}%
% east isomorphism with upper name
\newcommand{\Eiso}{\@ifnextchar[{\basicEiso}%
{\hspace{\SOURCE\unitlength}\basicEiso[\ARROWLENGTH]}}%
% basic east isomorphism with lower name
\def\basiceisO[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hisocase{\EAR}{\cong}{#2}{\Z}}%
% east isomorphism with lower name
\newcommand{\eisO}{\@ifnextchar[{\basiceisO}%
{\hspace{\SOURCE\unitlength}\basiceisO[\ARROWLENGTH]}}%
% basic east equality
\def\basiceeql[#1]{%
\Z=#1%
\multiply \Z by 100%
\hcase{\EEQL}{\Z}}%
% east equality
\newcommand{\eeql}{\@ifnextchar[{\basiceeql}%
{\hspace{\SOURCE\unitlength}\basiceeql[\ARROWLENGTH]}}%
% basic east equality with upper name
\def\basicEeql[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hcase{\EEQL}{\DUP{#2}}{\Z}}%
% east equality with upper name
\newcommand{\Eeql}{\@ifnextchar[{\basicEeql}%
{\hspace{\SOURCE\unitlength}\basicEeql[\ARROWLENGTH]}}%
% basic east equality with lower name
\def\basiceeqL[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\hcasE{\EEQL}{#2}{\Z}}%
% east equality with lower name
\newcommand{\eeqL}{\@ifnextchar[{\basiceeqL}%
{\hspace{\SOURCE\unitlength}\basiceeqL[\ARROWLENGTH]}}%
% basic pair of east arrows
\def\basicebiar[#1]{%
\Z=#1%
\multiply \Z by 100%
\hbicase{\EBIAR}{\Z}}%
% pair of east arrows
\newcommand{\ebiar}{\@ifnextchar[{\basicebiar}%
{\hspace{\SOURCE\unitlength}\basicebiar[\ARROWLENGTH]}}%
% basic pair of east arrows with names
\def\basicEbiar[#1]#2#3{%
\Z=#1%
\multiply \Z by 100%
\Hbicase{\EBIAR}{#2}{#3}{\Z}}%
% pair of east arrows with names
\newcommand{\Ebiar}{\@ifnextchar[{\basicEbiar}%
{\hspace{\SOURCE\unitlength}\basicEbiar[\ARROWLENGTH]}}%
\let\ebiaR=\Ebiar
% basic pair of east distributors
\def\basicebidist[#1]{%
\Z=#1%
\multiply \Z by 100%
\hbicase{\EBIDIST}{\Z}}%
% pair of east distributors
\newcommand{\ebidist}{\@ifnextchar[{\basicebidist}%
{\hspace{\SOURCE\unitlength}\basicebidist[\ARROWLENGTH]}}%
% basic pair of east distributors with names
\def\basicEbidist[#1]#2#3{%
\Z=#1%
\multiply \Z by 100%
\Hbicase{\EBIDIST}{\DUP{#2}}{\DDOWN{#3}}{\Z}}%
% pair of east distributors with names
\newcommand{\Ebidist}{\@ifnextchar[{\basicEbidist}%
{\hspace{\SOURCE\unitlength}\basicEbidist[\ARROWLENGTH]}}%
\let\ebidisT=\Ebidist
% basic pair of east adjoint arrows
\def\basiceadjar[#1]{%
\Z=#1%
\multiply \Z by 100%
\hbicase{\EADJAR}{\Z}}%
% pair of east adjoint arrows
\newcommand{\eadjar}{\@ifnextchar[{\basiceadjar}%
{\hspace{\SOURCE\unitlength}\basiceadjar[\ARROWLENGTH]}}%
% basic pair of east adjoint arrows with names
\def\basicEadjar[#1]#2#3{%
\Z=#1%
\multiply \Z by 100%
\Hbicase{\EADJAR}{#2}{#3}{\Z}}%
% pair of east adjoint arrows with names
\newcommand{\Eadjar}{\@ifnextchar[{\basicEadjar}%
{\hspace{\SOURCE\unitlength}\basicEadjar[\ARROWLENGTH]}}%
\let\eadjaR=\Eadjar
% basic pair of east adjoint distributors
\def\basiceadjdist[#1]{%
\Z=#1%
\multiply \Z by 100%
\hbicase{\EADJDIST}{\Z}}%
% pair of east adjoint distributors
\newcommand{\eadjdist}{\@ifnextchar[{\basiceadjdist}%
{\hspace{\SOURCE\unitlength}\basiceadjdist[\ARROWLENGTH]}}%
% basic pair of east adjoint distributors with names
\def\basicEadjdist[#1]#2#3{%
\Z=#1%
\multiply \Z by 100%
\Hbicase{\EADJDIST}{\DUP{#2}}{\DDOWN{#3}}{\Z}}%
% pair of east adjoint distributors with names
\newcommand{\Eadjdist}{\@ifnextchar[{\basicEadjdist}%
{\hspace{\SOURCE\unitlength}\basicEadjdist[\ARROWLENGTH]}}%
\let\eadjdisT=\Eadjdist
% WEST ARROWS
% \WAR{n} draws a pointing back arrow of length n units
\newcommand{\WAR}[1]%
{\begin{picture}(#1,0)%
\put(#1,0){\line(-1,0){#1}}%
\put(0,0){\whead}%
\end{picture}}%
% \WDIST{n} draws a pointing back distributor of length n units
\newcommand{\WDIST}[1]%
{\begin{picture}(#1,0)%
\put(#1,0){\line(-1,0){#1}}%
\put(0,0){\whead}%
\truex{400}%
\NUMBER=#1%
\divide\NUMBER by 2%
\put(\NUMBER,0){\circle{\value{x}}}%
\end{picture}}%
% \WDOTAR draws a dotted arrow of length n units
\newcommand{\WDOTAR}[1]%
{\truex{100}\truey{300}%
\NUMBEROFDOTS=#1%
\divide\NUMBEROFDOTS by \value{y}%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(#1,0)%
\multiput(#1,0)(-\value{y},0){\NUMBEROFDOTS}%
{\circle*{\value{x}}}%
\put(0,0){\whead}%
\end{picture}}%
% \WMONO{n} draws a pointing back monomorphism of length n units
\newcommand{\WMONO}[1]%
{\truetail%
\monolength=#1%
\advance\monolength by -\truemonotail%
\begin{picture}(#1,0)(-#1,0)%
\put(-\truemonotail,0){\line(-1,0){\monolength}}%
\put(-\truemonotail,0){\whead}%
\put(-#1,0){\whead}%
\end{picture}}%
% \WEPI{n} draws a pointing back epimorphism of length n units
\newcommand{\WEPI}[1]%
{\truehead%
\epilength=#1%
\advance\epilength by -\trueepihead%
\begin{picture}(#1,0)%
\put(#1,0){\line(-1,0){\epilength}}%
\put(\trueepihead,0){\whead}%
\put(0,0){\whead}%
\end{picture}}%
% \WBIMO{n} draws a pointing back bimorphism of length n units
\newcommand{\WBIMO}[1]%
{\truehead\truetail%
\monolength=#1
\advance\monolength by -\truemonotail%
\epilength=\monolength%
\advance\epilength by -\trueepihead%
\begin{picture}(#1,0)%
\put(\monolength,0){\line(-1,0){\epilength}}%
\put(\monolength,0){\whead}%
\put(\trueepihead,0){\whead}%
\put(0,0){\whead}%
\end{picture}}%
% \WBIAR{n} draws a pair of pointing back arrows of length n units
\newcommand{\WBIAR}[1]%
{\truex{700}%
\begin{picture}(#1,\value{x})%
\put(#1,0){\line(-1,0){#1}}%
\put(0,0){\whead}%
\put(#1,\value{x}){\line(-1,0){#1}}%
\put(0,\value{x}){\whead}%
\end{picture}}%
% \WBIDIST{n} draws a pair of pointing back distributors of length n units
\newcommand{\WBIDIST}[1]%
{\truex{700}%
\begin{picture}(#1,\value{x})%
\put(#1,0){\line(-1,0){#1}}%
\put(0,0){\whead}%
\put(#1,\value{x}){\line(-1,0){#1}}%
\put(0,\value{x}){\whead}%
\truey{400}%
\NUMBER=#1%
\divide\NUMBER by 2%
\put(\NUMBER,0){\circle{\value{y}}}%
\put(\NUMBER,\value{x}){\circle{\value{y}}}%
\end{picture}}%
% \WADJAR{n} draws a pair of adjoint arrows of length n units
\newcommand{\WADJAR}[1]%
{\truex{700}%
\begin{picture}(#1,\value{x})%
\put(0,\value{x}){\line(1,0){#1}}%
\put(#1,\value{x}){\ehead}%
\put(#1,0){\line(-1,0){#1}}%
\put(0,0){\whead}%
\end{picture}}%
% \WADJDIST{n} draws a pair of adjoint distributors of length n units
\newcommand{\WADJDIST}[1]%
{\truex{700}%
\begin{picture}(#1,\value{x})%
\put(0,\value{x}){\line(1,0){#1}}%
\put(#1,\value{x}){\ehead}%
\put(#1,0){\line(-1,0){#1}}%
\put(0,0){\whead}%
\truey{400}%
\NUMBER=#1%
\divide\NUMBER by 2%
\put(\NUMBER,0){\circle{\value{y}}}%
\put(\NUMBER,\value{x}){\circle{\value{y}}}%
\end{picture}}%
% All the following commands produce west arrows
% basic west arrow
\def\basicwar[#1]{%
\Z=#1%
\multiply \Z by 100%
\hcase{\WAR}{\Z}}%
% west arrow
\newcommand{\war}{\@ifnextchar[{\basicwar}%
{\hspace{\SOURCE\unitlength}\basicwar[\ARROWLENGTH]}}%
% basic west arrow with upper name
\def\basicWar[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hcase{\WAR}{#2}{\Z}}%
% west arrow with upper name
\newcommand{\War}{\@ifnextchar[{\basicWar}%
{\hspace{\SOURCE\unitlength}\basicWar[\ARROWLENGTH]}}%
% basic west arrow with lower name
\def\basicwaR[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\hcasE{\WAR}{#2}{\Z}}%
% west arrow with lower name
\newcommand{\waR}{\@ifnextchar[{\basicwaR}%
{\hspace{\SOURCE\unitlength}\basicwaR[\ARROWLENGTH]}}%
% basic west distributor
\def\basicwdist[#1]{%
\Z=#1%
\multiply \Z by 100%
\hcase{\WDIST}{\Z}}%
% west distributor
\newcommand{\wdist}{\@ifnextchar[{\basicwdist}%
{\hspace{\SOURCE\unitlength}\basicwdist[\ARROWLENGTH]}}%
% basic west distributor with upper name
\def\basicWdist[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hcase{\WDIST}{\DUP{#2}}{\Z}}%
% west distributor with upper name
\newcommand{\Wdist}{\@ifnextchar[{\basicWdist}%
{\hspace{\SOURCE\unitlength}\basicWdist[\ARROWLENGTH]}}%
% basic west distributor with lower name
\def\basicwdisT[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\hcasE{\WDIST}{\DDOWN{#2}}{\Z}}%
% west distributor with lower name
\newcommand{\wdisT}{\@ifnextchar[{\basicwdisT}%
{\hspace{\SOURCE\unitlength}\basicwdisT[\ARROWLENGTH]}}%
% basic west dotted arrow
\def\basicwdotar[#1]{%
\Z=#1%
\multiply \Z by 100%
\hcase{\WDOTAR}{\Z}}%
% west dotted arrow
\newcommand{\wdotar}{\@ifnextchar[{\basicwdotar}%
{\hspace{\SOURCE\unitlength}\basicwdotar[\ARROWLENGTH]}}%
% basic west dotted arrow with upper name
\def\basicWdotar[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hcase{\WDOTAR}{#2}{\Z}}%
% west dotted arrow with upper name
\newcommand{\Wdotar}{\@ifnextchar[{\basicWdotar}%
{\hspace{\SOURCE\unitlength}\basicWdotar[\ARROWLENGTH]}}%
% basic west dotted arrow with lower name
\def\basicwdotaR[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\hcasE{\WDOTAR}{#2}{\Z}}%
% west dotted arrow with lower name
\newcommand{\wdotaR}{\@ifnextchar[{\basicwdotaR}%
{\hspace{\SOURCE\unitlength}\basicwdotaR[\ARROWLENGTH]}}%
% basic west monomorphism
\def\basicwmono[#1]{%
\Z=#1%
\multiply \Z by 100%
\hcase{\WMONO}{\Z}}%
% west arrow
\newcommand{\wmono}{\@ifnextchar[{\basicwmono}%
{\hspace{\SOURCE\unitlength}\basicwmono[\ARROWLENGTH]}}%
% basic west monomorphism with upper name
\def\basicWmono[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hcase{\WMONO}{#2}{\Z}}%
% west monomorphism with upper name
\newcommand{\Wmono}{\@ifnextchar[{\basicWmono}%
{\hspace{\SOURCE\unitlength}\basicWmono[\ARROWLENGTH]}}%
% basic west monomorphism with lower name
\def\basicwmonO[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\hcasE{\WMONO}{#2}{\Z}}%
% west monomorphism with lower name
\newcommand{\wmonO}{\@ifnextchar[{\basicwmonO}%
{\hspace{\SOURCE\unitlength}\basicwmonO[\ARROWLENGTH]}}%
% basic west epimorphism
\def\basicwepi[#1]{%
\Z=#1%
\multiply \Z by 100%
\hcase{\WEPI}{\Z}}%
% west epimorphism
\newcommand{\wepi}{\@ifnextchar[{\basicwepi}%
{\hspace{\SOURCE\unitlength}\basicwepi[\ARROWLENGTH]}}%
% basic west epimorphism with upper name
\def\basicWepi[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hcase{\WEPI}{#2}{\Z}}%
% west epimorphism with upper name
\newcommand{\Wepi}{\@ifnextchar[{\basicWepi}%
{\hspace{\SOURCE\unitlength}\basicWepi[\ARROWLENGTH]}}%
% basic west epimorphism with lower name
\def\basicwepI[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\hcasE{\WEPI}{#2}{\Z}}%
% west epimorphism with lower name
\newcommand{\wepI}{\@ifnextchar[{\basicwepI}%
{\hspace{\SOURCE\unitlength}\basicwepI[\ARROWLENGTH]}}%
% basic west bimorphism
\def\basicwbimo[#1]{%
\Z=#1%
\multiply \Z by 100%
\hcase{\WBIMO}{\Z}}%
% west bimorphism
\newcommand{\wbimo}{\@ifnextchar[{\basicwbimo}%
{\hspace{\SOURCE\unitlength}\basicwbimo[\ARROWLENGTH]}}%
% basic west bimorphism with upper name
\def\basicWbimo[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hcase{\WBIMO}{#2}{\Z}}%
% west bimorphism with upper name
\newcommand{\Wbimo}{\@ifnextchar[{\basicWbimo}%
{\hspace{\SOURCE\unitlength}\basicWbimo[\ARROWLENGTH]}}%
% basic west bimorphism with lower name
\def\basicwbimO[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\hcasE{\WBIMO}{#2}{\Z}}%
% west bimorphism with lower name
\newcommand{\wbimO}{\@ifnextchar[{\basicwbimO}%
{\hspace{\SOURCE\unitlength}\basicwbimO[\ARROWLENGTH]}}%
% basic west isomorphism
\def\basicwiso[#1]{%
\Z=#1%
\multiply \Z by 100%
\Hisocase{\WAR}{\cong}{}{\Z}}%
% west isomorphism
\newcommand{\wiso}{\@ifnextchar[{\basicwiso}%
{\hspace{\SOURCE\unitlength}\basicwiso[\ARROWLENGTH]}}%
% basic west isomorphism with upper name
\def\basicWiso[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hisocase{\WAR}{#2}{\cong}{\Z}}%
% west isomorphism with upper name
\newcommand{\Wiso}{\@ifnextchar[{\basicWiso}%
{\hspace{\SOURCE\unitlength}\basicWiso[\ARROWLENGTH]}}%
% basic west isomorphism with lower name
\def\basicwisO[#1]#2{%
\Z=#1%
\multiply \Z by 100%
\Hisocase{\WAR}{\cong}{#2}{\Z}}%
% west isomorphism with lower name
\newcommand{\wisO}{\@ifnextchar[{\basicwisO}%
{\hspace{\SOURCE\unitlength}\basicwisO[\ARROWLENGTH]}}%
% west equality
\let\weql=\eeql%
% west equality with upper name
\let\Weql=\Eeql%
% west equality with lower name
\let\weqL=\eeqL%
% basic pair of west arrows
\def\basicwbiar[#1]{%
\Z=#1%
\multiply \Z by 100%
\hbicase{\WBIAR}{\Z}}%
% pair of west arrows
\newcommand{\wbiar}{\@ifnextchar[{\basicwbiar}%
{\hspace{\SOURCE\unitlength}\basicwbiar[\ARROWLENGTH]}}%
% basic pair of west arrows with names
\def\basicWbiar[#1]#2#3{%
\Z=#1%
\multiply \Z by 100%
\Hbicase{\WBIAR}{#2}{#3}{\Z}}%
% pair of west arrows with names
\newcommand{\Wbiar}{\@ifnextchar[{\basicWbiar}%
{\hspace{\SOURCE\unitlength}\basicWbiar[\ARROWLENGTH]}}%
\let\wbiaR=\Wbiar
% basic pair of west distributors
\def\basicwbidist[#1]{%
\Z=#1%
\multiply \Z by 100%
\hbicase{\WBIDIST}{\Z}}%
% pair of west distributors
\newcommand{\wbidist}{\@ifnextchar[{\basicwbidist}%
{\hspace{\SOURCE\unitlength}\basicwbidist[\ARROWLENGTH]}}%
% basic pair of west distributors with names
\def\basicWbidist[#1]#2#3{%
\Z=#1%
\multiply \Z by 100%
\Hbicase{\WBIDIST}{\DUP{#2}}{\DDOWN{#3}}{\Z}}%
% pair of west distributors with names
\newcommand{\Wbidist}{\@ifnextchar[{\basicWbidist}%
{\hspace{\SOURCE\unitlength}\basicWbidist[\ARROWLENGTH]}}%
\let\wbidisT=\Wbidist
% basic pair of west adjoint arrows
\def\basicwadjar[#1]{%
\Z=#1%
\multiply \Z by 100%
\hbicase{\WADJAR}{\Z}}%
% pair of west adjoint arrows
\newcommand{\wadjar}{\@ifnextchar[{\basicwadjar}%
{\hspace{\SOURCE\unitlength}\basicwadjar[\ARROWLENGTH]}}%
% basic pair of west adjoint arrows with names
\def\basicWadjar[#1]#2#3{%
\Z=#1%
\multiply \Z by 100%
\Hbicase{\WADJAR}{#2}{#3}{\Z}}%
% pair of west adjoint arrows with names
\newcommand{\Wadjar}{\@ifnextchar[{\basicWadjar}%
{\hspace{\SOURCE\unitlength}\basicWadjar[\ARROWLENGTH]}}%
\let\wadjaR=\Wadjar
% basic pair of west adjoint distributors
\def\basicwadjdist[#1]{%
\Z=#1%
\multiply \Z by 100%
\hbicase{\WADJDIST}{\Z}}%
% pair of west adjoint distributors
\newcommand{\wadjdist}{\@ifnextchar[{\basicwadjdist}%
{\hspace{\SOURCE\unitlength}\basicwadjdist[\ARROWLENGTH]}}%
% basic pair of west adjoint distributors with names
\def\basicWadjdist[#1]#2#3{%
\Z=#1%
\multiply \Z by 100%
\Hbicase{\WADJDIST}{\DUP{#2}}{\DDOWN{#3}}{\Z}}%
% pair of west adjoint distributors with names
\newcommand{\Wadjdist}{\@ifnextchar[{\basicWadjdist}%
{\hspace{\SOURCE\unitlength}\basicWadjdist[\ARROWLENGTH]}}%
\let\wadjdisT=\Wadjdist
% MACROS FOR DRAWING VERTICAL PICTURES
% \vcase{P}{n} draws the vertical picture P with length n units.
\newcommand{\vcase}[2]{\testdiagrammode#1{#2}}%
% \Vcase{P}{f}{n} draws the vertical picture P
% with left name f and length n units.
\newcommand{\Vcase}[3]{\testdiagrammode\makebox[0pt]%
{\makebox[0pt][r]{\raisebox{0pt}[0pt][0pt]{${#2}\hspace{2pt}$}}}#1{#3}}%
% \vcasE{P}{f}{n} draws the vertical picture P
% with right name f and length n units.
\newcommand{\vcasE}[3]{\testdiagrammode\makebox[0pt]%
{#1{#3}\makebox[0pt][l]{\raisebox{0pt}[0pt][0pt]{\hspace{2pt}$#2$}}}}%
% \Visocase{P}{f}{g}{n} draws the vertical picture P
% with names f, g and length n units.
\newcommand{\Visocase}[4]{\testdiagrammode\makebox[0pt]%
{\makebox[0pt][r]{\raisebox{0pt}[0pt][0pt]{$#2$\hspace{2pt}}}#1{#4}%
\makebox[0pt][l]{\raisebox{0pt}[0pt][0pt]{\hspace{2pt}$#3$}}}}%
% \vbicase{P}{n} draws the vertical bi-picture P with length n units.
\newcommand{\vbicase}[2]{\testdiagrammode\makebox[0pt]{{#1{#2}}}}%
% \Vbicase{P}{f}{g}{n} draws the vertical bi-picture P
% with names f, g and length n units.
\newcommand{\Vbicase}[4]{\testdiagrammode\makebox[0pt]%
{\makebox[0pt][r]{\raisebox{0pt}[0pt][0pt]{$#2$\hspace{5.5pt}}}#1{#4}%
\makebox[0pt][l]{\raisebox{0pt}[0pt][0pt]{\hspace{6.5pt}$#3$}}}}%
% SOUTH ARROWS
% \SAR{n} draws a south arrow of length n units
% and centers it in a box of width 0pt and height 0pt
\newcommand{\SAR}[1]%
{\begin{picture}(0,0)%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(0,#1){\line(0,-1){#1}}%
\put(0,0){\shead}%
\end{picture}}}\end{picture}}%
% \SDIST{n} draws a south distributor of length n units
% and centers it in a box of width 0pt and height 0pt
\newcommand{\SDIST}[1]%
{\begin{picture}(0,0)%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(0,#1){\line(0,-1){#1}}%
\put(0,0){\shead}%
\end{picture}}}%
\truex{400}%
\put(0,0){\circle{\value{x}}}%
\end{picture}}%
% \SDOTAR{n} draws a south dotted arrow of length n units
% and centers it in a box of width 0pt and height 0pt
\newcommand{\SDOTAR}[1]%
{\truex{100}\truey{300}%
\NUMBEROFDOTS=#1%
\divide\NUMBEROFDOTS by \value{y}%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(0,0)%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\multiput(0,#1)(0,-\value{y}){\NUMBEROFDOTS}%
{\circle*{\value{x}}}%
\put(0,0){\shead}%
\end{picture}}}\end{picture}}%
% \SMONO{n} draws a south monomorphism of length n units
% and centers it in a box of width 0pt and height 0pt
\newcommand{\SMONO}[1]%
{\truetail%
\monolength=#1%
\advance\monolength by -\truemonotail%
\begin{picture}(0,0)%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(0,\monolength){\line(0,-1){\monolength}}%
\put(0,\monolength){\shead}%
\put(0,0){\shead}%
\end{picture}}}\end{picture}}%
% \SEPI{n} draws a south epimorphism of length n units
% and centers it in a box of width 0pt and height 0pt
\newcommand{\SEPI}[1]%
{\truehead%
\epilength=#1%
\advance\epilength by -\trueepihead%
\begin{picture}(0,0)%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(0,#1){\line(0,-1){\epilength}}%
\put(0,\trueepihead){\shead}%
\put(0,0){\shead}%
\end{picture}}}\end{picture}}%
% \SBIMO{n} draws a south bimorphism of length n units
% and centers it in a box of width 0pt and height 0pt
\newcommand{\SBIMO}[1]%
{\truehead\truetail%
\monolength=#1%
\advance\monolength by -\truemonotail%
\epilength=\monolength%
\advance\epilength by -\trueepihead%
\begin{picture}(0,0)%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(0,\monolength){\line(0,-1){\epilength}}%
\put(0,\monolength){\shead}%
\put(0,\trueepihead){\shead}%
\put(0,0){\shead}%
\end{picture}}}\end{picture}}%
% \SBIAR{n} draws a pair of south arrows of length n units
% and centers it in a box of width 0pt and height 0pt
\newcommand{\SBIAR}[1]%
{\begin{picture}(0,0)%
\truex{350}%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(-\value{x},#1){\line(0,-1){#1}}%
\put(-\value{x},0){\shead}%
\put(\value{x},#1){\line(0,-1){#1}}%
\put(\value{x},0){\shead}%
\end{picture}}}\end{picture}}%
% \SBIDIST{n} draws a pair of south distributors of length n units
% and centers it in a box of width 0pt and height 0pt
\newcommand{\SBIDIST}[1]%
{\begin{picture}(0,0)%
\truex{350}%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(-\value{x},#1){\line(0,-1){#1}}%
\put(-\value{x},0){\shead}%
\put(\value{x},#1){\line(0,-1){#1}}%
\put(\value{x},0){\shead}%
\end{picture}}}%
\truey{400}%
\put(-\value{x},0){\circle{\value{y}}}%
\put(\value{x},0){\circle{\value{y}}}%
\end{picture}}%
% \SEQL{n} draws a vertical equality of length n units
% and centers it in a box of width 0pt and height 0pt
\newcommand{\SEQL}[1]%
{\begin{picture}(0,0)%
\truex{100}%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)\put(-\value{x},#1){\line(0,-1){#1}}%
\put(\value{x},#1){\line(0,-1){#1}}%
\end{picture}}}\end{picture}}%
% \SADJAR{n} draws a pair of vertical adjoint arrows of length n units
% and centers it in a box of width 0pt and height 0pt
\newcommand{\SADJAR}[1]{\begin{picture}(0,0)%
\truex{350}%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(-\value{x},#1){\line(0,-1){#1}}%
\put(-\value{x},0){\shead}%
\put(\value{x},0){\line(0,1){#1}}%
\put(\value{x},#1){\nhead}%
\end{picture}}}\end{picture}}%
% \SADJDIST{n} draws a pair of vertical adjoint distributors of length n units
% and centers it in a box of width 0pt and height 0pt
\newcommand{\SADJDIST}[1]{\begin{picture}(0,0)%
\truex{350}%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(-\value{x},#1){\line(0,-1){#1}}%
\put(-\value{x},0){\shead}%
\put(\value{x},0){\line(0,1){#1}}%
\put(\value{x},#1){\nhead}%
\end{picture}}}%
\truey{400}%
\put(-\value{x},0){\circle{\value{y}}}%
\put(\value{x},0){\circle{\value{y}}}%
\end{picture}}%
% All the following commands produce south arrows
% basic south arrow
\def\basicsar[#1]{\vcase{\SAR}{#100}}%
% south arrow
\newcommand{\sar}{\@ifnextchar[{\basicsar}{\basicsar[50]}}%
% basic south arrow with left name
\def\basicSar[#1]#2{\Vcase{\SAR}{#2}{#100}}%
% south arrow with left name
\newcommand{\Sar}{\@ifnextchar[{\basicSar}{\basicSar[50]}}%
% basic south arrow with right name
\def\basicsaR[#1]#2{\vcasE{\SAR}{#2}{#100}}%
% south arrow with right name
\newcommand{\saR}{\@ifnextchar[{\basicsaR}{\basicsaR[50]}}%
% basic south distributor
\def\basicsdist[#1]{\vcase{\SDIST}{#100}}%
% south distributor
\newcommand{\sdist}{\@ifnextchar[{\basicsdist}{\basicsdist[50]}}%
% basic south distributor with left name
\def\basicSdist[#1]#2{\Vcase{\SDIST}{#2\hspace*{2pt}}{#100}}%
% south distributor with left name
\newcommand{\Sdist}{\@ifnextchar[{\basicSdist}{\basicSdist[50]}}%
% basic south distributor with right name
\def\basicsdisT[#1]#2{\vcasE{\SDIST}{\hspace*{2pt}#2}{#100}}%
% south distributor with right name
\newcommand{\sdisT}{\@ifnextchar[{\basicsdisT}{\basicsdisT[50]}}%
% basic south dotted arrow
\def\basicsdotar[#1]{\vcase{\SDOTAR}{#100}}%
% south dotted arrow
\newcommand{\sdotar}{\@ifnextchar[{\basicsdotar}{\basicsdotar[50]}}%
% basic south dotted arrow with left name
\def\basicSdotar[#1]#2{\Vcase{\SDOTAR}{#2}{#100}}%
% south dotted arrow with left name
\newcommand{\Sdotar}{\@ifnextchar[{\basicSdotar}{\basicSdotar[50]}}%
% basic south dotted arrow with right name
\def\basicsdotaR[#1]#2{\vcasE{\SDOTAR}{#2}{#100}}%
% south dotted arrow with right name
\newcommand{\sdotaR}{\@ifnextchar[{\basicsdotaR}{\basicsdotaR[50]}}%
% basic south monomorphism
\def\basicsmono[#1]{\vcase{\SMONO}{#100}}%
% south arrow
\newcommand{\smono}{\@ifnextchar[{\basicsmono}{\basicsmono[50]}}%
% basic south monomorphism with left name
\def\basicSmono[#1]#2{\Vcase{\SMONO}{#2}{#100}}%
% south monomorphism with left name
\newcommand{\Smono}{\@ifnextchar[{\basicSmono}{\basicSmono[50]}}%
% basic south monomorphism with right name
\def\basicsmonO[#1]#2{\vcasE{\SMONO}{#2}{#100}}%
% south monomorphism with right name
\newcommand{\smonO}{\@ifnextchar[{\basicsmonO}{\basicsmonO[50]}}%
% basic south epimorphism
\def\basicsepi[#1]{\vcase{\SEPI}{#100}}%
% south epimorphism
\newcommand{\sepi}{\@ifnextchar[{\basicsepi}{\basicsepi[50]}}%
% basic south epimorphism with left name
\def\basicSepi[#1]#2{\Vcase{\SEPI}{#2}{#100}}%
% south epimorphism with left name
\newcommand{\Sepi}{\@ifnextchar[{\basicSepi}{\basicSepi[50]}}%
% basic south epimorphism with right name
\def\basicsepI[#1]#2{\vcasE{\SEPI}{#2}{#100}}%
% south epimorphism with right name
\newcommand{\sepI}{\@ifnextchar[{\basicsepI}{\basicsepI[50]}}%
% basic south bimorphism
\def\basicsbimo[#1]{\vcase{\SBIMO}{#100}}%
% south bimorphism
\newcommand{\sbimo}{\@ifnextchar[{\basicsbimo}{\basicsbimo[50]}}%
% basic south bimorphism with left name
\def\basicSbimo[#1]#2{\Vcase{\SBIMO}{#2}{#100}}%
% south bimorphism with left name
\newcommand{\Sbimo}{\@ifnextchar[{\basicSbimo}{\basicSbimo[50]}}%
% basic south bimorphism with right name
\def\basicsbimO[#1]#2{\vcasE{\SBIMO}{#2}{#100}}%
% south bimorphism with right name
\newcommand{\sbimO}{\@ifnextchar[{\basicsbimO}{\basicsbimO[50]}}%
% basic south isomorphism
\def\basicsiso[#1]{\Visocase{\SAR}{\cong}{}{#100}}%
% south isomorphism
\newcommand{\siso}{\@ifnextchar[{\basicsiso}{\basicsiso[50]}}%
% basic south isomorphism with left name
\def\basicSiso[#1]#2{\Visocase{\SAR}{#2}{\cong}{#100}}%
% south isomorphism with left name
\newcommand{\Siso}{\@ifnextchar[{\basicSiso}{\basicSiso[50]}}%
% basic south isomorphism with right name
\def\basicsisO[#1]#2{\Visocase{\SAR}{\cong}{#2}{#100}}%
% south isomorphism with right name
\newcommand{\sisO}{\@ifnextchar[{\basicsisO}{\basicsisO[50]}}%
% basic south equality
\def\basicseql[#1]{\vcase{\SEQL}{#100}}%
% south equality
\newcommand{\seql}{\@ifnextchar[{\basicseql}{\basicseql[50]}}%
% basic south equality with left name
\def\basicSeql[#1]#2{\Vcase{\SEQL}{#2\hspace*{2pt}}{#100}}%
% south equality with left name
\newcommand{\Seql}{\@ifnextchar[{\basicSeql}{\basicSeql[50]}}%
% basic south equality with right name
\def\basicseqL[#1]#2{\vcasE{\SEQL}{\hspace*{2pt}#2}{#100}}%
% south equality with right name
\newcommand{\seqL}{\@ifnextchar[{\basicseqL}{\basicseqL[50]}}%
% basic pair of south arrows
\def\basicsbiar[#1]{\vbicase{\SBIAR}{#100}}%
% pair of south arrows
\newcommand{\sbiar}{\@ifnextchar[{\basicsbiar}{\basicsbiar[50]}}%
% basic pair of south arrows with names
\def\basicSbiar[#1]#2#3{\Vbicase{\SBIAR}{#2}{#3}{#100}}%
% pair of south arrows with names
\newcommand{\Sbiar}{\@ifnextchar[{\basicSbiar}{\basicSbiar[50]}}%
\let\sbiaR=\Sbiar
% basic pair of south distributors
\def\basicsbidist[#1]{\vbicase{\SBIDIST}{#100}}%
% pair of south distributors
\newcommand{\sbidist}{\@ifnextchar[{\basicsbidist}{\basicsbidist[50]}}%
% basic pair of south distributors with names
\def\basicSbidist[#1]#2#3%
{\Vbicase{\SBIDIST}{#2\hspace*{2pt}}{\hspace*{2pt}#3}{#100}}%
% pair of south distributors with names
\newcommand{\Sbidist}{\@ifnextchar[{\basicSbidist}{\basicSbidist[50]}}%
\let\sbidisT=\Sbidist
% basic pair of south adjoint arrows
\def\basicsadjar[#1]{\vbicase{\SADJAR}{#100}}%
% pair of south adjoint arrows
\newcommand{\sadjar}{\@ifnextchar[{\basicsadjar}{\basicsadjar[50]}}%
% basic pair of south adjoint arrows with names
\def\basicSadjar[#1]#2#3{\Vbicase{\SADJAR}{#2}{#3}{#100}}%
% pair of south adjoint arrows with names
\newcommand{\Sadjar}{\@ifnextchar[{\basicSadjar}{\basicSadjar[50]}}%
\let\sadjaR=\Sadjar
% basic pair of south adjoint distributors
\def\basicsadjdist[#1]{\vbicase{\SADJDIST}{#100}}%
% pair of south adjoint distributors
\newcommand{\sadjdist}{\@ifnextchar[{\basicsadjdist}{\basicsadjdist[50]}}%
% basic pair of south adjoint distributors with names
\def\basicSadjdist[#1]#2#3%
{\Vbicase{\SADJDIST}{#2\hspace*{2pt}}{\hspace*{2pt}#3}{#100}}%
% pair of south adjoint distributors with names
\newcommand{\Sadjdist}{\@ifnextchar[{\basicSadjdist}{\basicSadjdist[50]}}%
\let\sadjdisT=\Sadjdist
% NORTH ARROWS
% \NAR{n} draws a north arrow of length n pt
% and centers it in a box of width 0pt and height 0pt
\newcommand{\NAR}[1]%
{\begin{picture}(0,0)%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(0,0){\line(0,1){#1}}%
\put(0,#1){\nhead}%
\end{picture}}}\end{picture}}%
% \NDIST{n} draws a north distributor of length n pt
% and centers it in a box of width 0pt and height 0pt
\newcommand{\NDIST}[1]%
{\begin{picture}(0,0)%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(0,0){\line(0,1){#1}}%
\put(0,#1){\nhead}%
\end{picture}}}
\truex{400}%
\put(0,0){\circle{\value{x}}}%
\end{picture}}%
% \NDOTAR{n} draws a north dotted arrow of length n units
% and centers it in a box of width 0pt and height 0pt
\newcommand{\NDOTAR}[1]%
{\truex{100}\truey{300}%
\NUMBEROFDOTS=#1%
\divide\NUMBEROFDOTS by \value{y}%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(0,0)%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\multiput(0,0)(0,\value{y}){\NUMBEROFDOTS}%
{\circle*{\value{x}}}%
\put(0,#1){\nhead}%
\end{picture}}}\end{picture}}%
% \NMONO{n} draws a north monomorphism of length n pt
% and centers it in a box of width 0pt and height 0pt
\newcommand{\NMONO}[1]%
{\truetail%
\monolength=#1%
\advance\monolength by -\truemonotail%
\begin{picture}(0,0)%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(0,\truemonotail){\line(0,1){\monolength}}%
\put(0,#1){\nhead}%
\put(0,\truemonotail){\nhead}%
\end{picture}}}\end{picture}}%
% \NEPI{n} draws a north epimorphism of length n pt
% and centers it in a box of width 0pt and height 0pt
\newcommand{\NEPI}[1]%
{\truehead%
\epilength=#1%
\advance\epilength by -\trueepihead%
\begin{picture}(0,0)%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(0,0){\line(0,1){\epilength}}%
\put(0,#1){\nhead}%
\put(0,\epilength){\nhead}%
\end{picture}}}\end{picture}}%
% \NBIMO{n} draws a north bimorphism of length n pt
% and centers it in a box of width 0pt and height 0pt
\newcommand{\NBIMO}[1]%
{\truehead\truetail%
\epilength=#1%
\advance\epilength by -\trueepihead%
\monolength=\epilength%
\advance\monolength by -\truemonotail%
\begin{picture}(0,0)%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(0,\truemonotail){\line(0,1){\monolength}}%
\put(0,#1){\nhead}%
\put(0,\truemonotail){\nhead}%
\put(0,\epilength){\nhead}%
\end{picture}}}\end{picture}}%
% \NBIAR{n} draws a pair of north arrows of length n pt
% and centers it in a box of width 0pt and height 0pt
\newcommand{\NBIAR}[1]%
{\begin{picture}(0,0)%
\truex{350}%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(-\value{x},0){\line(0,1){#1}}%
\put(-\value{x},#1){\nhead}%
\put(\value{x},0){\line(0,1){#1}}%
\put(\value{x},#1){\nhead}%
\end{picture}}}\end{picture}}%
% \NBIDIST{n} draws a pair of north distributors of length n pt
% and centers it in a box of width 0pt and height 0pt
\newcommand{\NBIDIST}[1]%
{\begin{picture}(0,0)%
\truex{350}%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(-\value{x},0){\line(0,1){#1}}%
\put(-\value{x},#1){\nhead}%
\put(\value{x},0){\line(0,1){#1}}%
\put(\value{x},#1){\nhead}%
\end{picture}}}
\truey{400}%
\put(-\value{x},0){\circle{\value{y}}}%
\put(\value{x},0){\circle{\value{y}}}%
\end{picture}}%
% \NADJAR{n} draws a pair of vertical adjoint arrows of length n pt
% and centers it in a box of width 0pt and height 0pt
\newcommand{\NADJAR}[1]{\begin{picture}(0,0)%
\truex{350}%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(\value{x},#1){\line(0,-1){#1}}%
\put(\value{x},0){\shead}%
\put(-\value{x},0){\line(0,1){#1}}%
\put(-\value{x},#1){\nhead}%
\end{picture}}}\end{picture}}%
% \NADJDIST{n} draws a pair of vertical adjoint distributors of length n pt
% and centers it in a box of width 0pt and height 0pt
\newcommand{\NADJDIST}[1]{\begin{picture}(0,0)%
\truex{350}%
\put(0,0){\makebox(0,0)%
{\begin{picture}(0,#1)%
\put(\value{x},#1){\line(0,-1){#1}}%
\put(\value{x},0){\shead}%
\put(-\value{x},0){\line(0,1){#1}}%
\put(-\value{x},#1){\nhead}%
\end{picture}}}
\truey{400}%
\put(-\value{x},0){\circle{\value{y}}}%
\put(\value{x},0){\circle{\value{y}}}%
\end{picture}}%
% All the following commands produce north arrows
% basic north arrow
\def\basicnar[#1]{\vcase{\NAR}{#100}}%
% north arrow
\newcommand{\nar}{\@ifnextchar[{\basicnar}{\basicnar[50]}}%
% basic north arrow with left name
\def\basicNar[#1]#2{\Vcase{\NAR}{#2}{#100}}%
% north arrow with left name
\newcommand{\Nar}{\@ifnextchar[{\basicNar}{\basicNar[50]}}%
% basic north arrow with right name
\def\basicnaR[#1]#2{\vcasE{\NAR}{#2}{#100}}%
% north arrow with right name
\newcommand{\naR}{\@ifnextchar[{\basicnaR}{\basicnaR[50]}}%
% basic north distributor
\def\basicndist[#1]{\vcase{\NDIST}{#100}}%
% north distributor
\newcommand{\ndist}{\@ifnextchar[{\basicndist}{\basicndist[50]}}%
% basic north distributor with left name
\def\basicNdist[#1]#2{\Vcase{\NDIST}{#2\hspace*{2pt}}{#100}}%
% north distributor with left name
\newcommand{\Ndist}{\@ifnextchar[{\basicNdist}{\basicNdist[50]}}%
% basic north distributor with right name
\def\basicndisT[#1]#2{\vcasE{\NDIST}{\hspace*{2pt}#2}{#100}}%
% north distributor with right name
\newcommand{\ndisT}{\@ifnextchar[{\basicndisT}{\basicndisT[50]}}%
% basic north dotted arrow
\def\basicndotar[#1]{\vcase{\NDOTAR}{#100}}%
% north dotted arrow
\newcommand{\ndotar}{\@ifnextchar[{\basicndotar}{\basicndotar[50]}}%
% basic north dotted arrow with left name
\def\basicNdotar[#1]#2{\Vcase{\NDOTAR}{#2}{#100}}%
% north dotted arrow with left name
\newcommand{\Ndotar}{\@ifnextchar[{\basicNdotar}{\basicNdotar[50]}}%
% basic north dotted arrow with right name
\def\basicndotaR[#1]#2{\vcasE{\NDOTAR}{#2}{#100}}%
% north dotted arrow with right name
\newcommand{\ndotaR}{\@ifnextchar[{\basicndotaR}{\basicndotaR[50]}}%
% basic north monomorphism
\def\basicnmono[#1]{\vcase{\NMONO}{#100}}%
% north arrow
\newcommand{\nmono}{\@ifnextchar[{\basicnmono}%
{\basicnmono[50]}}%
% basic north monomorphism with left name
\def\basicNmono[#1]#2{\Vcase{\NMONO}{#2}{#100}}%
% north monomorphism with left name
\newcommand{\Nmono}{\@ifnextchar[{\basicNmono}{\basicNmono[50]}}%
% basic north monomorphism with right name
\def\basicnmonO[#1]#2{\vcasE{\NMONO}{#2}{#100}}%
% north monomorphism with right name
\newcommand{\nmonO}{\@ifnextchar[{\basicnmonO}{\basicnmonO[50]}}%
% basic north epimorphism
\def\basicnepi[#1]{\vcase{\NEPI}{#100}}%
% north epimorphism
\newcommand{\nepi}{\@ifnextchar[{\basicnepi}{\basicnepi[50]}}%
% basic north epimorphism with left name
\def\basicNepi[#1]#2{\Vcase{\NEPI}{#2}{#100}}%
% north epimorphism with left name
\newcommand{\Nepi}{\@ifnextchar[{\basicNepi}{\basicNepi[50]}}%
% basic north epimorphism with right name
\def\basicnepI[#1]#2{\vcasE{\NEPI}{#2}{#100}}%
% north epimorphism with right name
\newcommand{\nepI}{\@ifnextchar[{\basicnepI}{\basicnepI[50]}}%
% basic north bimorphism
\def\basicnbimo[#1]{\vcase{\NBIMO}{#100}}%
% north bimorphism
\newcommand{\nbimo}{\@ifnextchar[{\basicnbimo}{\basicnbimo[50]}}%
% basic north bimorphism with left name
\def\basicNbimo[#1]#2{\Vcase{\NBIMO}{#2}{#100}}%
% north bimorphism with left name
\newcommand{\Nbimo}{\@ifnextchar[{\basicNbimo}{\basicNbimo[50]}}%
% basic north bimorphism with right name
\def\basicnbimO[#1]#2{\vcasE{\NBIMO}{#2}{#100}}%
% north bimorphism with right name
\newcommand{\nbimO}{\@ifnextchar[{\basicnbimO}{\basicnbimO[50]}}%
% basic north isomorphism
\def\basicniso[#1]{\Visocase{\NAR}{\cong}{}{#100}}%
% north isomorphism
\newcommand{\niso}{\@ifnextchar[{\basicniso}{\basicniso[50]}}%
% basic north isomorphism with left name
\def\basicNiso[#1]#2{\Visocase{\NAR}{#2}{\cong}{#100}}%
% north isomorphism with left name
\newcommand{\Niso}{\@ifnextchar[{\basicNiso}{\basicNiso[50]}}%
% basic north isomorphism with right name
\def\basicnisO[#1]#2{\Visocase{\NAR}{\cong}{#2}{#100}}%
% north isomorphism with right name
\newcommand{\nisO}{\@ifnextchar[{\basicnisO}{\basicnisO[50]}}%
% north equality
\let\neql=\seql%
% north equality with left name
\let\Neql=\Seql%
% north equality with right name
\let\neqL=\seqL%
% basic pair of north arrows
\def\basicnbiar[#1]{\vbicase{\NBIAR}{#100}}%
% pair of north arrows
\newcommand{\nbiar}{\@ifnextchar[{\basicnbiar}{\basicnbiar[50]}}%
% basic pair of north arrows with names
\def\basicNbiar[#1]#2#3{\Vbicase{\NBIAR}{#2}{#3}{#100}}%
% pair of north arrows with names
\newcommand{\Nbiar}{\@ifnextchar[{\basicNbiar}{\basicNbiar[50]}}%
\let\nbiaR=\Nbiar
% basic pair of north distributors
\def\basicnbidist[#1]{\vbicase{\NBIDIST}{#100}}%
% pair of north distributors
\newcommand{\nbidist}{\@ifnextchar[{\basicnbidist}{\basicnbidist[50]}}%
% basic pair of north distributors with names
\def\basicNbidist[#1]#2#3%
{\Vbicase{\NBIDIST}{#2\hspace*{2pt}}{\hspace*{2pt}#3}{#100}}%
% pair of north distributors with names
\newcommand{\Nbidist}{\@ifnextchar[{\basicNbidist}{\basicNbidist[50]}}%
\let\nbidisT=\Nbidist
% basic pair of north adjoint arrows
\def\basicnadjar[#1]{\vbicase{\NADJAR}{#100}}%
% pair of north adjoint arrows
\newcommand{\nadjar}{\@ifnextchar[{\basicnadjar}{\basicnadjar[50]}}%
% basic pair of north adjoint arrows with names
\def\basicNadjar[#1]#2#3{\Vbicase{\NADJAR}{#2}{#3}{#100}}%
% pair of north adjoint arrows with names
\newcommand{\Nadjar}{\@ifnextchar[{\basicNadjar}{\basicNadjar[50]}}%
\let\nadjaR=\Nadjar
% basic pair of north adjoint distributors
\def\basicnadjdist[#1]{\vbicase{\NADJDIST}{#100}}%
% pair of north adjoint distributors
\newcommand{\nadjdist}{\@ifnextchar[{\basicnadjdist}{\basicnadjdist[50]}}%
% basic pair of north adjoint distributors with names
\def\basicNadjdist[#1]#2#3%
{\Vbicase{\NADJDIST}{#2\hspace*{2pt}}{\hspace*{2pt}#3}{#100}}%
% pair of north adjoint distributors with names
\newcommand{\Nadjdist}{\@ifnextchar[{\basicNadjdist}{\basicNadjdist[50]}}%
\let\nadjdisT=\Nadjdist
% MACROS FOR FIRST DIAGONAL PICTURES
% \fdcase{P}{f}{g}{n} draws the picture P with names f, g
% and length n units
\newcommand{\fdcase}[4]{\testdiagrammode\begin{picture}(0,0)%
\put(0,0){#1{#4}}%
\truex{200}\truey{600}\truez{600}%
\put(-\value{x},-\value{x}){\makebox(0,\value{z})[r]{${#2}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#3}$}}%
\end{picture}}%
% \fdbicase{P}{f}{g}{n} draws the bipicture P with names f, g
% and length n units
\newcommand{\fdbicase}[4]{\testdiagrammode\begin{picture}(0,0)%
\put(0,0){#1{#4}}%
\truex{900}\truey{150}%
\put(-\value{x},\value{y}){${#2}$}%
\truex{300}\truey{1050}%
\put(\value{x},-\value{y}){${#3}$}%
\end{picture}}%
% NORTH-EAST ARROWS
% \NEAR{n} draws a north-east arrow of length nx100 units
\newcommand{\NEAR}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(-\Y,-\Y){\line(1,1){#1}}%
\put(\Y,\Y){\nehead}%
\end{picture}}%
% \NEDIST{n} draws a north-east distributor of length n units
\newcommand{\NEDIST}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(-\Y,-\Y){\line(1,1){#1}}%
\put(\Y,\Y){\nehead}%
\truex{400}%
\put(0,0){\circle{\value{x}}}%
\end{picture}}%
% \NEDOTAR{n} draws a north-east dotted arrow of length n units
\newcommand{\NEDOTAR}[1]%
{\truex{100}\truey{212}%
\Y=#1%
\divide\Y by 2%
\NUMBEROFDOTS=#1%
\divide\NUMBEROFDOTS by \value{y}%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(0,0)%
\multiput(-\Y,-\Y)(\value{y},\value{y}){\NUMBEROFDOTS}%
{\circle*{\value{x}}}%
\put(\Y,\Y){\nehead}%
\end{picture}}%
% \NEMONO{n} draws a north-east monomorphism of length n units
\newcommand{\NEMONO}[1]{%
\Y=#1%
\divide \Y by 2%
\Truetail%
\bimolength=#1%
\advance\bimolength by -\Truemonotail%
\monolength=\bimolength%
\advance\monolength by -\Y%
\begin{picture}(0,0)%
\put(-\monolength,-\monolength){\line(1,1){\bimolength}}%
\put(-\monolength,-\monolength){\nehead}%
\put(\Y,\Y){\nehead}%
\end{picture}}%
% \NEEPI{n} draws a north-east epimorphism of length n units
\newcommand{\NEEPI}[1]{%
\Y=#1%
\divide\Y by 2%
\Truehead%
\bimolength=#1%
\advance\bimolength by -\Trueepihead%
\epilength=\bimolength%
\advance\epilength by -\Y%
\begin{picture}(0,0)%
\put(-\Y,-\Y){\line(1,1){\bimolength}}%
\put(\epilength,\epilength){\nehead}%
\put(\Y,\Y){\nehead}%
\end{picture}}%
% \NEBIMO{n} draws a north-east bimorphism of length n units
\newcommand{\NEBIMO}[1]{%
\Y=#1%
\divide\Y by 2%
\Truetail\Truehead%
\bimolength=#1%
\advance\bimolength by -\Truemonotail%
\monolength=\bimolength%
\advance\monolength by -\Y%
\advance\bimolength by -\Trueepihead%
\epilength=\bimolength%
\advance\epilength by -\monolength%
\begin{picture}(0,0)%
\put(-\monolength,-\monolength){\line(1,1){\bimolength}}%
\put(-\monolength,-\monolength){\nehead}%
\put(\epilength,\epilength){\nehead}%
\put(\Y,\Y){\nehead}%
\end{picture}}%
% \NEBIAR{n} draws a pair of north-east arrows of length n units
\newcommand{\NEBIAR}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(-\Y,-\Y){\begin{picture}(0,0)%
\truex{247}%
\put(-\value{x},\value{x}){\line(1,1){#1}}%
\put(\value{x},-\value{x}){\line(1,1){#1}}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(\monolength,\epilength){\nehead}%
\put(\epilength,\monolength){\nehead}%
\end{picture}}\end{picture}}%
% \NEBIDIST{n} draws a pair of north-east distributors of length n units
\newcommand{\NEBIDIST}[1]{%
\Y=#1%
\divide\Y by 2%
\truey{400}%
\begin{picture}(0,0)%
\put(-\Y,-\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(\value{x},-\value{x}){\line(1,1){#1}}%
\put(\epilength,\monolength){\nehead}%
\end{picture}}%
\put(-\Y,-\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by \value{x}%
\epilength=#1%
\advance\epilength by -\value{x}%
\put(-\value{x},\value{x}){\line(1,1){#1}}%
\put(\epilength,\monolength){\nehead}%
\end{picture}}%
\put(-\value{x},\value{x}){\circle{\value{y}}}%
\put(\value{x},-\value{x}){\circle{\value{y}}}%
\end{picture}}%
% \NEEQL{n} draws a north-east equality of length n units
\newcommand{\NEEQL}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(-\Y,-\Y){\begin{picture}(0,0)%
\truex{70}%
\put(-\value{x},\value{x}){\line(1,1){#1}}%
\put(\value{x},-\value{x}){\line(1,1){#1}}%
\end{picture}}\end{picture}}%
% \NEADJAR{n} draws a north-east pair of adjoint arrows of length n units
\newcommand{\NEADJAR}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(-\Y,-\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(\value{x},-\value{x}){\line(1,1){#1}}%
\put(\epilength,\monolength){\nehead}%
\end{picture}}%
\put(\Y,\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(-\value{x},\value{x}){\line(-1,-1){#1}}%
\put(-\epilength,-\monolength){\swhead}%
\end{picture}}\end{picture}}%
% \NEADJDIST{n} draws a north-east pair of adjoint distributors of length n units
\newcommand{\NEADJDIST}[1]{%
\Y=#1%
\divide\Y by 2%
\truey{400}%
\begin{picture}(0,0)%
\put(-\Y,-\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(\value{x},-\value{x}){\line(1,1){#1}}%
\put(\epilength,\monolength){\nehead}%
\end{picture}}%
\put(\Y,\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(-\value{x},\value{x}){\line(-1,-1){#1}}%
\put(-\epilength,-\monolength){\swhead}%
\end{picture}}%
\put(-\value{x},\value{x}){\circle{\value{y}}}%
\put(\value{x},-\value{x}){\circle{\value{y}}}%
\end{picture}}%
% All the following commands draw north-east arrows
% north-east arrow of length nx100 units
\def\basicnear[#1]{\fdcase{\NEAR}{}{}{#100}}%
% north-east arrow
\newcommand{\near}{\@ifnextchar[{\basicnear}{\basicnear[59]}}%
% north-east arrow with upper name [1] and length nx100 units
\def\basicNear[#1]#2{\fdcase{\NEAR}{#2}{}{#100}}%
% north-east arrow with upper name
\newcommand{\Near}{\@ifnextchar[{\basicNear}{\basicNear[59]}}%
% north-east arrow with lower name [1] and length nx100 units
\def\basicneaR[#1]#2{\fdcase{\NEAR}{}{#2}{#100}}%
% north-east arrow with lower name [1]
\newcommand{\neaR}{\@ifnextchar[{\basicneaR}{\basicneaR[59]}}%
% north-east distributor of length nx100 units
\def\basicnedist[#1]{\fdcase{\NEDIST}{}{}{#100}}%
% north-east distributor
\newcommand{\nedist}{\@ifnextchar[{\basicnedist}{\basicnedist[59]}}%
% north-east distributor with upper name [1] and length nx100 units
\def\basicNedist[#1]#2{\fdcase{\NEDIST}{#2}{}{#100}}%
% north-east distributor with upper name
\newcommand{\Nedist}{\@ifnextchar[{\basicNedist}{\basicNedist[59]}}%
% north-east distributor with lower name [1] and length nx100 units
\def\basicnedisT[#1]#2{\fdcase{\NEDIST}{}{#2}{#100}}%
% north-east distributor with lower name [1]
\newcommand{\nedisT}{\@ifnextchar[{\basicnedisT}{\basicnedisT[59]}}%
% north-east dotted arrow of length nx100 units
\def\basicnedotar[#1]{\fdcase{\NEDOTAR}{}{}{#100}}%
% north-east dotted arrow
\newcommand{\nedotar}{\@ifnextchar[{\basicnedotar}{\basicnedotar[59]}}%
% north-east dotted arrow with upper name [1] and length nx100 units
\def\basicNedotar[#1]#2{\fdcase{\NEDOTAR}{#2}{}{#100}}%
% north-east dotted arrow with upper name
\newcommand{\Nedotar}{\@ifnextchar[{\basicNedotar}{\basicNedotar[59]}}%
% north-east dotted arrow with lower name [1] and length nx100 units
\def\basicnedotaR[#1]#2{\fdcase{\NEDOTAR}{}{#2}{#100}}%
% north-east dotted arrow with lower name [1]
\newcommand{\nedotaR}{\@ifnextchar[{\basicnedotaR}{\basicnedotaR[59]}}%
% north-east monomorphism of length nx100 units
\def\basicnemono[#1]{\fdcase{\NEMONO}{}{}{#100}}%
% north-east monomorphism
\newcommand{\nemono}{\@ifnextchar[{\basicnemono}{\basicnemono[59]}}%
% north-east monomorphism with upper name [1] and length nx100 units
\def\basicNemono[#1]#2{\fdcase{\NEMONO}{#2}{}{#100}}%
% north-east monomophism with upper name
\newcommand{\Nemono}{\@ifnextchar[{\basicNemono}{\basicNemono[59]}}%
% north-east monomorphism with lower name [1] and length nx100 units
\def\basicnemonO[#1]#2{\fdcase{\NEMONO}{}{#2}{#100}}%
% north-east monomorphism with lower name [1]
\newcommand{\nemonO}{\@ifnextchar[{\basicnemonO}{\basicnemonO[59]}}%
% north-east epimorphism of length nx100 units
\def\basicneepi[#1]{\fdcase{\NEEPI}{}{}{#100}}%
% north-east epimorphism
\newcommand{\neepi}{\@ifnextchar[{\basicneepi}{\basicneepi[59]}}%
% north-east epimorphism with upper name [1] and length nx100 units
\def\basicNeepi[#1]#2{\fdcase{\NEEPI}{#2}{}{#100}}%
% north-east epimorphism with upper name
\newcommand{\Neepi}{\@ifnextchar[{\basicNeepi}{\basicNeepi[59]}}%
% north-east epimorphism with lower name [1] and length nx100 units
\def\basicneepI[#1]#2{\fdcase{\NEEPI}{}{#2}{#100}}%
% north-east epimorphism with lower name [1]
\newcommand{\neepI}{\@ifnextchar[{\basicneepI}{\basicneepI[59]}}%
% north-east bimorphism of length nx100 units
\def\basicnebimo[#1]{\fdcase{\NEBIMO}{}{}{#100}}%
% north-east bimorphism
\newcommand{\nebimo}{\@ifnextchar[{\basicnebimo}{\basicnebimo[59]}}%
% north-east bimorphism with upper name [1] and length nx100 units
\def\basicNebimo[#1]#2{\fdcase{\NEBIMO}{#2}{}{#100}}%
% north-east bimorphism with upper name
\newcommand{\Nebimo}{\@ifnextchar[{\basicNebimo}{\basicNebimo[59]}}%
% north-east bimorphism with lower name [1] and length nx100 units
\def\basicnebimO[#1]#2{\fdcase{\NEBIMO}{}{#2}{#100}}%
% north-east bimorphism with lower name [1]
\newcommand{\nebimO}{\@ifnextchar[{\basicnebimO}{\basicnebimO[59]}}%
% north-east isomorphism of length nx100 units
\def\basicneiso[#1]{\fdcase{\NEAR}{\hspace{-2pt}\cong}{}{#100}}%
% north-east isomorphism
\newcommand{\neiso}{\@ifnextchar[{\basicneiso}{\basicneiso[59]}}%
% north-east isomorphism with upper name [1] and length nx100 units
\def\basicNeiso[#1]#2{\fdcase{\NEAR}{#2}{\cong}{#100}}%
% north-east isomorphism with upper name
\newcommand{\Neiso}{\@ifnextchar[{\basicNeiso}{\basicNeiso[59]}}%
% north-east isomorphism with lower name [1] and length nx100 units
\def\basicneisO[#1]#2{\fdcase{\NEAR}{\hspace{-2pt}\cong}{#2}{#100}}%
% north-east isomorphism with lower name [1]
\newcommand{\neisO}{\@ifnextchar[{\basicneisO}{\basicneisO[59]}}%
% north-east equality of length nx100 units
\def\basicneeql[#1]{\fdcase{\NEEQL}{}{}{#100}}%
% north-east equality
\newcommand{\neeql}{\@ifnextchar[{\basicneeql}{\basicneeql[59]}}%
% north-east equality with upper name [1] and length nx100 units
\def\basicNeeql[#1]#2{\fdcase{\NEEQL}{#2}{}{#100}}%
% north-east equality with upper name
\newcommand{\Neeql}{\@ifnextchar[{\basicNeeql}{\basicNeeql[59]}}%
% north-east equality with lower name [1] and length nx100 units
\def\basicneeqL[#1]#2{\fdcase{\NEEQL}{}{#2}{#100}}%
% north-east equality with lower name [1]
\newcommand{\neeqL}{\@ifnextchar[{\basicneeqL}{\basicneeqL[59]}}%
% pair of north-east arrows of length nx100 units
\def\basicnebiar[#1]{\fdbicase{\NEBIAR}{}{}{#100}}%
% pair of north-east arrows
\newcommand{\nebiar}{\@ifnextchar[{\basicnebiar}{\basicnebiar[59]}}%
% pair of north-east arrows with names [1][2] and length nx100 units
\def\basicNebiar[#1]#2#3{\fdbicase{\NEBIAR}{#2}{#3}{#100}}%
% pair of north-east arrows with names
\newcommand{\Nebiar}{\@ifnextchar[{\basicNebiar}{\basicNebiar[59]}}%
\let\nebiaR=\Nebiar
% pair of north-east adjoint arrows of length nx100 units
\def\basicneadjar[#1]{\fdbicase{\NEADJAR}{}{}{#100}}%
% pair of north-east adjoint arrows
\newcommand{\neadjar}{\@ifnextchar[{\basicneadjar}{\basicneadjar[59]}}%
% pair of north-east adjoint arrows with names [1][2] and length nx100 units
\def\basicNeadjar[#1]#2#3{\fdbicase{\NEADJAR}{#2}{#3}{#100}}%
% pair of north-east adjoint arrows with names
\newcommand{\Neadjar}{\@ifnextchar[{\basicNeadjar}{\basicNeadjar[59]}}%
\let\neadjaR=\Neadjar
% pair of north-east distributors of length nx100 units
\def\basicnebidist[#1]{\fdbicase{\NEBIDIST}{}{}{#100}}%
% pair of north-east distributors
\newcommand{\nebidist}{\@ifnextchar[{\basicnebidist}{\basicnebidist[59]}}%
% pair of north-east distributors with names [1][2] and length nx100 units
\def\basicNebidist[#1]#2#3{\fdbicase{\NEBIDIST}{#2}{#3}{#100}}%
% pair of north-east distributors with names
\newcommand{\Nebidist}{\@ifnextchar[{\basicNebidist}{\basicNebidist[59]}}%
\let\nebidisT=\Nebidist
% pair of north-east adjoint distributors of length nx100 units
\def\basicneadjdist[#1]{\fdbicase{\NEADJDIST}{}{}{#100}}%
% pair of north-east adjoint distributors
\newcommand{\neadjdist}{\@ifnextchar[{\basicneadjdist}{\basicneadjdist[59]}}%
% pair of north-east adjoint distributors with names [1][2] and length nx100 units
\def\basicNeadjdist[#1]#2#3{\fdbicase{\NEADJDIST}{#2}{#3}{#100}}%
% pair of north-east adjoint distributors with names
\newcommand{\Neadjdist}{\@ifnextchar[{\basicNeadjdist}{\basicNeadjdist[59]}}%
\let\neadjdisT=\Neadjdist
% SOUT-WEST ARROWS
% \SWAR{n} draws a south-west arrow of length nx100 units
\newcommand{\SWAR}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(\Y,\Y){\line(-1,-1){#1}}%
\put(-\Y,-\Y){\swhead}%
\end{picture}}%
% \SWDIST{n} draws a south-west distributor of length n units
\newcommand{\SWDIST}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(\Y,\Y){\line(-1,-1){#1}}%
\put(-\Y,-\Y){\swhead}%
\truex{400}%
\put(0,0){\circle{\value{x}}}%
\end{picture}}%
% \SWDOTAR{n} draws a south-west dotted arrow of length n units
\newcommand{\SWDOTAR}[1]%
{\truex{100}\truey{212}%
\Y=#1%
\divide\Y by 2%
\NUMBEROFDOTS=#1%
\divide\NUMBEROFDOTS by \value{y}%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(0,0)%
\multiput(\Y,\Y)(-\value{y},-\value{y}){\NUMBEROFDOTS}%
{\circle*{\value{x}}}%
\put(-\Y,-\Y){\swhead}%
\end{picture}}%
% \SWMONO{n} draws a south-west monomorphism of length n units
\newcommand{\SWMONO}[1]{%
\Y=#1%
\divide \Y by 2%
\Truetail%
\bimolength=#1%
\advance\bimolength by -\Truemonotail%
\monolength=\bimolength%
\advance\monolength by -\Y%
\begin{picture}(0,0)%
\put(\monolength,\monolength){\line(-1,-1){\bimolength}}%
\put(\monolength,\monolength){\swhead}%
\put(-\Y,-\Y){\swhead}%
\end{picture}}%
% \SWEPI{n} draws a south-west epimorphism of length n units
\newcommand{\SWEPI}[1]{%
\Y=#1%
\divide\Y by 2%
\Truehead%
\bimolength=#1%
\advance\bimolength by -\Trueepihead%
\epilength=\bimolength%
\advance\epilength by -\Y%
\begin{picture}(0,0)%
\put(\Y,\Y){\line(-1,-1){\bimolength}}%
\put(-\epilength,-\epilength){\swhead}%
\put(-\Y,-\Y){\swhead}%
\end{picture}}%
% \SWBIMO{n} draws a south-west bimorphism of length n units
\newcommand{\SWBIMO}[1]{%
\Y=#1%
\divide\Y by 2%
\Truetail\Truehead%
\bimolength=#1%
\advance\bimolength by -\Truemonotail%
\monolength=\bimolength%
\advance\monolength by -\Y%
\advance\bimolength by -\Trueepihead%
\epilength=\bimolength%
\advance\epilength by -\monolength%
\begin{picture}(0,0)%
\put(\monolength,\monolength){\line(-1,-1){\bimolength}}%
\put(\monolength,\monolength){\swhead}%
\put(-\epilength,-\epilength){\swhead}%
\put(-\Y,-\Y){\swhead}%
\end{picture}}%
% \SWBIAR{n} draws a pair of south-west arrows of length n units
\newcommand{\SWBIAR}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(\Y,\Y){\begin{picture}(0,0)%
\truex{247}%
\put(\value{x},-\value{x}){\line(-1,-1){#1}}%
\put(-\value{x},\value{x}){\line(-1,-1){#1}}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(-\monolength,-\epilength){\swhead}%
\put(-\epilength,-\monolength){\swhead}%
\end{picture}}\end{picture}}%
% \SWBIDIST{n} draws a pair of south-west distributors of length n units
\newcommand{\SWBIDIST}[1]{%
\Y=#1%
\divide\Y by 2%
\truey{400}%
\begin{picture}(0,0)%
\put(\Y,\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(-\value{x},\value{x}){\line(-1,-1){#1}}%
\put(-\epilength,-\monolength){\swhead}%
\end{picture}}%
\put(\Y,\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by \value{x}%
\epilength=#1%
\advance\epilength by -\value{x}%
\put(\value{x},-\value{x}){\line(-1,-1){#1}}%
\put(-\epilength,-\monolength){\swhead}%
\end{picture}}%
\put(\value{x},-\value{x}){\circle{\value{y}}}%
\put(-\value{x},\value{x}){\circle{\value{y}}}%
\end{picture}}%
% \SWADJAR{n} draws a south-west pair of adjoint arrows of length n units
\newcommand{\SWADJAR}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(\Y,\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(\value{x},-\value{x}){\line(-1,-1){#1}}%
\put(-\monolength,-\epilength){\swhead}%
\end{picture}}%
\put(-\Y,-\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(-\value{x},\value{x}){\line(1,1){#1}}%
\put(\monolength,\epilength){\nehead}%
\end{picture}}\end{picture}}%
% \SWADJDIST{n} draws a south-west pair of adjoint distributors of length n units
\newcommand{\SWADJDIST}[1]{%
\Y=#1%
\divide\Y by 2%
\truey{400}%
\begin{picture}(0,0)%
\put(\Y,\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(\value{x},-\value{x}){\line(-1,-1){#1}}%
\put(-\monolength,-\epilength){\swhead}%
\end{picture}}%
\put(-\Y,-\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(-\value{x},\value{x}){\line(1,1){#1}}%
\put(\monolength,\epilength){\nehead}%
\end{picture}}%
\put(-\value{x},\value{x}){\circle{\value{y}}}%
\put(\value{x},-\value{x}){\circle{\value{y}}}%
\end{picture}}%
% All the following commands draw south-west arrows
% south-west arrow of length nx100 units
\def\basicswar[#1]{\fdcase{\SWAR}{}{}{#100}}%
% south-west arrow
\newcommand{\swar}{\@ifnextchar[{\basicswar}{\basicswar[59]}}%
% south-west arrow with upper name [1] and length nx100 units
\def\basicSwar[#1]#2{\fdcase{\SWAR}{#2}{}{#100}}%
% south-west arrow with upper name
\newcommand{\Swar}{\@ifnextchar[{\basicSwar}{\basicSwar[59]}}%
% south-west arrow with lower name [1] and length nx100 units
\def\basicswaR[#1]#2{\fdcase{\SWAR}{}{#2}{#100}}%
% south-west arrow with lower name [1]
\newcommand{\swaR}{\@ifnextchar[{\basicswaR}{\basicswaR[59]}}%
% south-west distributor of length nx100 units
\def\basicswdist[#1]{\fdcase{\SWDIST}{}{}{#100}}%
% south-west distributor
\newcommand{\swdist}{\@ifnextchar[{\basicswdist}{\basicswdist[59]}}%
% south-west distributor with upper name [1] and length nx100 units
\def\basicSwdist[#1]#2{\fdcase{\SWDIST}{#2}{}{#100}}%
% south-west distributor with upper name
\newcommand{\Swdist}{\@ifnextchar[{\basicSwdist}{\basicSwdist[59]}}%
% south-west distributor with lower name [1] and length nx100 units
\def\basicswdisT[#1]#2{\fdcase{\SWDIST}{}{#2}{#100}}%
% south-west distributor with lower name [1]
\newcommand{\swdisT}{\@ifnextchar[{\basicswdisT}{\basicswdisT[59]}}%
% south-west dotted arrow of length nx100 units
\def\basicswdotar[#1]{\fdcase{\SWDOTAR}{}{}{#100}}%
% south-west dotted arrow
\newcommand{\swdotar}{\@ifnextchar[{\basicswdotar}{\basicswdotar[59]}}%
% south-west dotted arrow with upper name [1] and length nx100 units
\def\basicSwdotar[#1]#2{\fdcase{\SWDOTAR}{#2}{}{#100}}%
% south-west dotted arrow with upper name
\newcommand{\Swdotar}{\@ifnextchar[{\basicSwdotar}{\basicSwdotar[59]}}%
% south-west dotted arrow with lower name [1] and length nx100 units
\def\basicswdotaR[#1]#2{\fdcase{\SWDOTAR}{}{#2}{#100}}%
% south-west dotted arrow with lower name [1]
\newcommand{\swdotaR}{\@ifnextchar[{\basicswdotaR}{\basicswdotaR[59]}}%
% south-west monomorphism of length nx100 units
\def\basicswmono[#1]{\fdcase{\SWMONO}{}{}{#100}}%
% south-west monomorphism
\newcommand{\swmono}{\@ifnextchar[{\basicswmono}{\basicswmono[59]}}%
% south-west monomorphism with upper name [1] and length nx100 units
\def\basicSwmono[#1]#2{\fdcase{\SWMONO}{#2}{}{#100}}%
% south-west monomophism with upper name
\newcommand{\Swmono}{\@ifnextchar[{\basicSwmono}{\basicSwmono[59]}}%
% south-west monomorphism with lower name [1] and length nx100 units
\def\basicswmonO[#1]#2{\fdcase{\SWMONO}{}{#2}{#100}}%
% south-west monomorphism with lower name [1]
\newcommand{\swmonO}{\@ifnextchar[{\basicswmonO}{\basicswmonO[59]}}%
% south-west epimorphism of length nx100 units
\def\basicswepi[#1]{\fdcase{\SWEPI}{}{}{#100}}%
% south-west epimorphism
\newcommand{\swepi}{\@ifnextchar[{\basicswepi}{\basicswepi[59]}}%
% south-west epimorphism with upper name [1] and length nx100 units
\def\basicSwepi[#1]#2{\fdcase{\SWEPI}{#2}{}{#100}}%
% south-west epimorphism with upper name
\newcommand{\Swepi}{\@ifnextchar[{\basicSwepi}{\basicSwepi[59]}}%
% south-west epimorphism with lower name [1] and length nx100 units
\def\basicswepI[#1]#2{\fdcase{\SWEPI}{}{#2}{#100}}%
% south-west epimorphism with lower name [1]
\newcommand{\swepI}{\@ifnextchar[{\basicswepI}{\basicswepI[59]}}%
% south-west bimorphism of length nx100 units
\def\basicswbimo[#1]{\fdcase{\SWBIMO}{}{}{#100}}%
% south-west bimorphism
\newcommand{\swbimo}{\@ifnextchar[{\basicswbimo}{\basicswbimo[59]}}%
% south-west bimorphism with upper name [1] and length nx100 units
\def\basicSwbimo[#1]#2{\fdcase{\SWBIMO}{#2}{}{#100}}%
% south-west bimorphism with upper name
\newcommand{\Swbimo}{\@ifnextchar[{\basicSwbimo}{\basicSwbimo[59]}}%
% south-west bimorphism with lower name [1] and length nx100 units
\def\basicswbimO[#1]#2{\fdcase{\SWBIMO}{}{#2}{#100}}%
% south-west bimorphism with lower name [1]
\newcommand{\swbimO}{\@ifnextchar[{\basicswbimO}{\basicswbimO[59]}}%
% south-west isomorphism of length nx100 units
\def\basicswiso[#1]{\fdcase{\SWAR}{\hspace{-2pt}\cong}{}{#100}}%
% south-west isomorphism
\newcommand{\swiso}{\@ifnextchar[{\basicswiso}{\basicswiso[59]}}%
% south-west isomorphism with upper name [1] and length nx100 units
\def\basicSwiso[#1]#2{\fdcase{\SWAR}{#2}{\cong}{#100}}%
% south-west isomorphism with upper name
\newcommand{\Swiso}{\@ifnextchar[{\basicSwiso}{\basicSwiso[59]}}%
% south-west isomorphism with lower name [1] and length nx100 units
\def\basicswisO[#1]#2{\fdcase{\SWAR}{\hspace{-2pt}\cong}{#2}{#100}}%
% south-west isomorphism with lower name [1]
\newcommand{\swisO}{\@ifnextchar[{\basicswisO}{\basicswisO[59]}}%
% south-west equality
\let\sweql\neeql%
% south-west equality with upper name [1]
\let\Sweql=\Neeql%
% south-west equality with lower name [1]
\let\sweqL=\neeqL%
% pair of south-west arrows of length nx100 units
\def\basicswbiar[#1]{\fdbicase{\SWBIAR}{}{}{#100}}%
% pair of south-west arrows
\newcommand{\swbiar}{\@ifnextchar[{\basicswbiar}{\basicswbiar[59]}}%
% pair of south-west arrows with names [1][2] and length nx100 units
\def\basicSwbiar[#1]#2#3{\fdbicase{\SWBIAR}{#2}{#3}{#100}}%
% pair of south-west arrows with names
\newcommand{\Swbiar}{\@ifnextchar[{\basicSwbiar}{\basicSwbiar[59]}}%
\let\swbiaR=\Swbiar
% pair of south-west adjoint arrows of length nx100 units
\def\basicswadjar[#1]{\fdbicase{\SWADJAR}{}{}{#100}}%
% pair of south-west adjoint arrows
\newcommand{\swadjar}{\@ifnextchar[{\basicswadjar}{\basicswadjar[59]}}%
% pair of south-west adjoint arrows with names [1][2] and length nx100 units
\def\basicSwadjar[#1]#2#3{\fdbicase{\SWADJAR}{#2}{#3}{#100}}%
% pair of south-west adjoint arrows with names
\newcommand{\Swadjar}{\@ifnextchar[{\basicSwadjar}{\basicSwadjar[59]}}%
\let\swadjaR=\Swadjar
% pair of south-west distributors of length nx100 units
\def\basicswbidist[#1]{\fdbicase{\SWBIDIST}{}{}{#100}}%
% pair of south-west distributors
\newcommand{\swbidist}{\@ifnextchar[{\basicswbidist}{\basicswbidist[59]}}%
% pair of south-west distributors with names [1][2] and length nx100 units
\def\basicSwbidist[#1]#2#3{\fdbicase{\SWBIDIST}{#2}{#3}{#100}}%
% pair of south-west distributors with names
\newcommand{\Swbidist}{\@ifnextchar[{\basicSwbidist}{\basicSwbidist[59]}}%
\let\swbidisT=\Swbidist
% pair of south-west adjoint distributors of length nx100 units
\def\basicswadjdist[#1]{\fdbicase{\SWADJDIST}{}{}{#100}}%
% pair of south-west adjoint distributors
\newcommand{\swadjdist}{\@ifnextchar[{\basicswadjdist}{\basicswadjdist[59]}}%
% pair of south-west adjoint distributors with names [1][2] and length nx100 units
\def\basicSwadjdist[#1]#2#3{\fdbicase{\SWADJDIST}{#2}{#3}{#100}}%
% pair of south-west adjoint distributors with names
\newcommand{\Swadjdist}{\@ifnextchar[{\basicSwadjdist}{\basicSwadjdist[59]}}%
\let\swadjdisT=\Swadjdist
% MACROS FOR SECOND DIAGONAL PICTURES
% \sdcase{P}{f}{g}{n} draws the picture P with names f, g
% and length n units
\newcommand{\sdcase}[4]{\testdiagrammode\begin{picture}(0,0)%
\put(0,0){#1{#4}}%
\truex{100}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#2}$}}%
\truex{300}\truey{800}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#3}$}}%
\end{picture}}%
% \sdbicase{P}{f}{g}{n} draws the bipicture P with names f, g
% and length n units
\newcommand{\sdbicase}[4]{\testdiagrammode\begin{picture}(0,0)%
\put(0,0){#1{#4}}%
\truex{350}\truey{600}\truez{950}%
\put(\value{x},\value{x}){\makebox(0,\value{y})[l]{${#2}$}}%
\truex{450}\truey{600}\truez{1050}%
\put(-\value{x},-\value{z}){\makebox(0,\value{y})[r]{${#3}$}}%
\end{picture}}%
% SOUTH-EAST ARROWS
% \SEAR{n} draws a south-east arrow of length nx100 units
\newcommand{\SEAR}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(-\Y,\Y){\line(1,-1){#1}}%
\put(\Y,-\Y){\sehead}%
\end{picture}}%
% \SEDIST{n} draws a south-east distributor of length n units
\newcommand{\SEDIST}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(-\Y,\Y){\line(1,-1){#1}}%
\put(\Y,-\Y){\sehead}%
\truex{400}%
\put(0,0){\circle{\value{x}}}%
\end{picture}}%
% \SEDOTAR{n} draws a south-east dotted arrow of length n units
\newcommand{\SEDOTAR}[1]%
{\truex{100}\truey{212}%
\Y=#1%
\divide\Y by 2%
\NUMBEROFDOTS=#1%
\divide\NUMBEROFDOTS by \value{y}%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(0,0)%
\multiput(-\Y,\Y)(\value{y},-\value{y}){\NUMBEROFDOTS}%
{\circle*{\value{x}}}%
\put(\Y,-\Y){\sehead}%
\end{picture}}%
% \SEMONO{n} draws a south-east monomorphism of length n units
\newcommand{\SEMONO}[1]{%
\Y=#1%
\divide \Y by 2%
\Truetail%
\bimolength=#1%
\advance\bimolength by -\Truemonotail%
\monolength=\bimolength%
\advance\monolength by -\Y%
\begin{picture}(0,0)%
\put(-\monolength,\monolength){\line(1,-1){\bimolength}}%
\put(-\monolength,\monolength){\sehead}%
\put(\Y,-\Y){\sehead}%
\end{picture}}%
% \SEEPI{n} draws a south-east epimorphism of length n units
\newcommand{\SEEPI}[1]{%
\Y=#1%
\divide\Y by 2%
\Truehead%
\bimolength=#1%
\advance\bimolength by -\Trueepihead%
\epilength=\bimolength%
\advance\epilength by -\Y%
\begin{picture}(0,0)%
\put(-\Y,\Y){\line(1,-1){\bimolength}}%
\put(\epilength,-\epilength){\sehead}%
\put(\Y,-\Y){\sehead}%
\end{picture}}%
% \SEBIMO{n} draws a south-east bimorphism of length n units
\newcommand{\SEBIMO}[1]{%
\Y=#1%
\divide\Y by 2%
\Truetail\Truehead%
\bimolength=#1%
\advance\bimolength by -\Truemonotail%
\monolength=\bimolength%
\advance\monolength by -\Y%
\advance\bimolength by -\Trueepihead%
\epilength=\bimolength%
\advance\epilength by -\monolength%
\begin{picture}(0,0)%
\put(-\monolength,\monolength){\line(1,-1){\bimolength}}%
\put(-\monolength,\monolength){\sehead}%
\put(\epilength,-\epilength){\sehead}%
\put(\Y,-\Y){\sehead}%
\end{picture}}%
% \SEBIAR{n} draws a pair of south-east arrows of length n units
\newcommand{\SEBIAR}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(-\Y,\Y){\begin{picture}(0,0)%
\truex{247}%
\put(-\value{x},-\value{x}){\line(1,-1){#1}}%
\put(\value{x},\value{x}){\line(1,-1){#1}}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(\monolength,-\epilength){\sehead}%
\put(\epilength,-\monolength){\sehead}%
\end{picture}}\end{picture}}%
% \SEBIDIST{n} draws a pair of south-east distributors of length n units
\newcommand{\SEBIDIST}[1]{%
\Y=#1%
\divide\Y by 2%
\truey{400}%
\begin{picture}(0,0)%
\put(-\Y,\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(\value{x},\value{x}){\line(1,-1){#1}}%
\put(\epilength,-\monolength){\sehead}%
\end{picture}}%
\put(-\Y,\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by \value{x}%
\epilength=#1%
\advance\epilength by -\value{x}%
\put(-\value{x},-\value{x}){\line(1,-1){#1}}%
\put(\epilength,-\monolength){\sehead}%
\end{picture}}%
\put(-\value{x},-\value{x}){\circle{\value{y}}}%
\put(\value{x},\value{x}){\circle{\value{y}}}%
\end{picture}}%
% \SEEQL{n} draws a south-east equality of length n units
\newcommand{\SEEQL}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(-\Y,\Y){\begin{picture}(0,0)%
\truex{70}%
\put(-\value{x},-\value{x}){\line(1,-1){#1}}%
\put(\value{x},\value{x}){\line(1,-1){#1}}%
\end{picture}}\end{picture}}%
% \SEADJAR{n} draws a south-east pair of adjoint arrows of length n units
\newcommand{\SEADJAR}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(-\Y,\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(-\value{x},-\value{x}){\line(1,-1){#1}}%
\put(\monolength,-\epilength){\sehead}%
\end{picture}}%
\put(\Y,-\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(\value{x},\value{x}){\line(-1,1){#1}}%
\put(-\monolength,\epilength){\nwhead}%
\end{picture}}\end{picture}}%
% \SEADJDIST{n} draws a south-east pair of adjoint distributors of length n units
\newcommand{\SEADJDIST}[1]{%
\Y=#1%
\divide\Y by 2%
\truey{400}%
\begin{picture}(0,0)%
\put(-\Y,\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(-\value{x},-\value{x}){\line(1,-1){#1}}%
\put(\monolength,-\epilength){\sehead}%
\end{picture}}%
\put(\Y,-\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(\value{x},\value{x}){\line(-1,1){#1}}%
\put(-\monolength,\epilength){\nwhead}%
\end{picture}}%
\put(-\value{x},-\value{x}){\circle{\value{y}}}%
\put(\value{x},\value{x}){\circle{\value{y}}}%
\end{picture}}%
% All the following commands draw south-east arrows
% south-east arrow of length nx100 units
\def\basicsear[#1]{\sdcase{\SEAR}{}{}{#100}}%
% south-east arrow
\newcommand{\sear}{\@ifnextchar[{\basicsear}{\basicsear[59]}}%
% south-east arrow with upper name [1] and length nx100 units
\def\basicSear[#1]#2{\sdcase{\SEAR}{#2}{}{#100}}%
% south-east arrow with upper name
\newcommand{\Sear}{\@ifnextchar[{\basicSear}{\basicSear[59]}}%
% south-east arrow with lower name [1] and length nx100 units
\def\basicseaR[#1]#2{\sdcase{\SEAR}{}{#2}{#100}}%
% south-east arrow with lower name [1]
\newcommand{\seaR}{\@ifnextchar[{\basicseaR}{\basicseaR[59]}}%
% south-east distributor of length nx100 units
\def\basicsedist[#1]{\sdcase{\SEDIST}{}{}{#100}}%
% south-east distributor
\newcommand{\sedist}{\@ifnextchar[{\basicsedist}{\basicsedist[59]}}%
% south-east distributor with upper name [1] and length nx100 units
\def\basicSedist[#1]#2{\sdcase{\SEDIST}{#2}{}{#100}}%
% south-east distributor with upper name
\newcommand{\Sedist}{\@ifnextchar[{\basicSedist}{\basicSedist[59]}}%
% south-east distributor with lower name [1] and length nx100 units
\def\basicsedisT[#1]#2{\sdcase{\SEDIST}{}{#2}{#100}}%
% south-east distributor with lower name [1]
\newcommand{\sedisT}{\@ifnextchar[{\basicsedisT}{\basicsedisT[59]}}%
% south-east dotted arrow of length nx100 units
\def\basicsedotar[#1]{\sdcase{\SEDOTAR}{}{}{#100}}%
% south-east dotted arrow
\newcommand{\sedotar}{\@ifnextchar[{\basicsedotar}{\basicsedotar[59]}}%
% south-east dotted arrow with upper name [1] and length nx100 units
\def\basicSedotar[#1]#2{\sdcase{\SEDOTAR}{#2}{}{#100}}%
% south-east dotted arrow with upper name
\newcommand{\Sedotar}{\@ifnextchar[{\basicSedotar}{\basicSedotar[59]}}%
% south-east dotted arrow with lower name [1] and length nx100 units
\def\basicsedotaR[#1]#2{\sdcase{\SEDOTAR}{}{#2}{#100}}%
% south-east dotted arrow with lower name [1]
\newcommand{\sedotaR}{\@ifnextchar[{\basicsedotaR}{\basicsedotaR[59]}}%
% south-east monomorphism of length nx100 units
\def\basicsemono[#1]{\sdcase{\SEMONO}{}{}{#100}}%
% south-east monomorphism
\newcommand{\semono}{\@ifnextchar[{\basicsemono}{\basicsemono[59]}}%
% south-east monomorphism with upper name [1] and length nx100 units
\def\basicSemono[#1]#2{\sdcase{\SEMONO}{#2}{}{#100}}%
% south-east monomophism with upper name
\newcommand{\Semono}{\@ifnextchar[{\basicSemono}{\basicSemono[59]}}%
% south-east monomorphism with lower name [1] and length nx100 units
\def\basicsemonO[#1]#2{\sdcase{\SEMONO}{}{#2}{#100}}%
% south-east monomorphism with lower name [1]
\newcommand{\semonO}{\@ifnextchar[{\basicsemonO}{\basicsemonO[59]}}%
% south-east epimorphism of length nx100 units
\def\basicseepi[#1]{\sdcase{\SEEPI}{}{}{#100}}%
% south-east epimorphism
\newcommand{\seepi}{\@ifnextchar[{\basicseepi}{\basicseepi[59]}}%
% south-east epimorphism with upper name [1] and length nx100 units
\def\basicSeepi[#1]#2{\sdcase{\SEEPI}{#2}{}{#100}}%
% south-east epimorphism with upper name
\newcommand{\Seepi}{\@ifnextchar[{\basicSeepi}{\basicSeepi[59]}}%
% south-east epimorphism with lower name [1] and length nx100 units
\def\basicseepI[#1]#2{\sdcase{\SEEPI}{}{#2}{#100}}%
% south-east epimorphism with lower name [1]
\newcommand{\seepI}{\@ifnextchar[{\basicseepI}{\basicseepI[59]}}%
% south-east bimorphism of length nx100 units
\def\basicsebimo[#1]{\sdcase{\SEBIMO}{}{}{#100}}%
% south-east bimorphism
\newcommand{\sebimo}{\@ifnextchar[{\basicsebimo}{\basicsebimo[59]}}%
% south-east bimorphism with upper name [1] and length nx100 units
\def\basicSebimo[#1]#2{\sdcase{\SEBIMO}{#2}{}{#100}}%
% south-east bimorphism with upper name
\newcommand{\Sebimo}{\@ifnextchar[{\basicSebimo}{\basicSebimo[59]}}%
% south-east bimorphism with lower name [1] and length nx100 units
\def\basicsebimO[#1]#2{\sdcase{\SEBIMO}{}{#2}{#100}}%
% south-east bimorphism with lower name [1]
\newcommand{\sebimO}{\@ifnextchar[{\basicsebimO}{\basicsebimO[59]}}%
% south-east isomorphism of length nx100 units
\def\basicseiso[#1]{\sdcase{\SEAR}{\hspace{-2pt}\cong}{}{#100}}%
% south-east isomorphism
\newcommand{\seiso}{\@ifnextchar[{\basicseiso}{\basicseiso[59]}}%
% south-east isomorphism with upper name [1] and length nx100 units
\def\basicSeiso[#1]#2{\sdcase{\SEAR}{#2}{\cong}{#100}}%
% south-east isomorphism with upper name
\newcommand{\Seiso}{\@ifnextchar[{\basicSeiso}{\basicSeiso[59]}}%
% south-east isomorphism with lower name [1] and length nx100 units
\def\basicseisO[#1]#2{\sdcase{\SEAR}{\hspace{-2pt}\cong}{#2}{#100}}%
% south-east isomorphism with lower name [1]
\newcommand{\seisO}{\@ifnextchar[{\basicseisO}{\basicseisO[59]}}%
% south-east equality of length nx100 units
\def\basicseeql[#1]{\sdcase{\SEEQL}{}{}{#100}}%
% south-east equality
\newcommand{\seeql}{\@ifnextchar[{\basicseeql}{\basicseeql[59]}}%
% south-east equality with upper name [1] and length nx100 units
\def\basicSeeql[#1]#2{\sdcase{\SEEQL}{#2}{}{#100}}%
% south-east equality with upper name
\newcommand{\Seeql}{\@ifnextchar[{\basicSeeql}{\basicSeeql[59]}}%
% south-east equality with lower name [1] and length nx100 units
\def\basicseeqL[#1]#2{\sdcase{\SEEQL}{}{#2}{#100}}%
% south-east equality with lower name [1]
\newcommand{\seeqL}{\@ifnextchar[{\basicseeqL}{\basicseeqL[59]}}%
% pair of south-east arrows of length nx100 units
\def\basicsebiar[#1]{\sdbicase{\SEBIAR}{}{}{#100}}%
% pair of south-east arrows
\newcommand{\sebiar}{\@ifnextchar[{\basicsebiar}{\basicsebiar[59]}}%
% pair of south-east arrows with names [1][2] and length nx100 units
\def\basicSebiar[#1]#2#3{\sdbicase{\SEBIAR}{#2}{#3}{#100}}%
% pair of south-east arrows with names
\newcommand{\Sebiar}{\@ifnextchar[{\basicSebiar}{\basicSebiar[59]}}%
\let\sebiaR=\Sebiar
% pair of south-east adjoint arrows of length nx100 units
\def\basicseadjar[#1]{\sdbicase{\SEADJAR}{}{}{#100}}%
% pair of south-east adjoint arrows
\newcommand{\seadjar}{\@ifnextchar[{\basicseadjar}{\basicseadjar[59]}}%
% pair of south-east adjoint arrows with names [1][2] and length nx100 units
\def\basicSeadjar[#1]#2#3{\sdbicase{\SEADJAR}{#2}{#3}{#100}}%
% pair of south-east adjoint arrows with names
\newcommand{\Seadjar}{\@ifnextchar[{\basicSeadjar}{\basicSeadjar[59]}}%
\let\seadjaR=\Seadjar
% pair of south-east distributors of length nx100 units
\def\basicsebidist[#1]{\sdbicase{\SEBIDIST}{}{}{#100}}%
% pair of south-east distributors
\newcommand{\sebidist}{\@ifnextchar[{\basicsebidist}{\basicsebidist[59]}}%
% pair of south-east distributors with names [1][2] and length nx100 units
\def\basicSebidist[#1]#2#3{\sdbicase{\SEBIDIST}{#2}{#3}{#100}}%
% pair of south-east distributors with names
\newcommand{\Sebidist}{\@ifnextchar[{\basicSebidist}{\basicSebidist[59]}}%
\let\sebidisT=\Sebidist
% pair of south-east adjoint distributors of length nx100 units
\def\basicseadjdist[#1]{\sdbicase{\SEADJDIST}{}{}{#100}}%
% pair of south-east adjoint distributors
\newcommand{\seadjdist}{\@ifnextchar[{\basicseadjdist}{\basicseadjdist[59]}}%
% pair of south-east adjoint distributors with names [1][2] and length nx100 units
\def\basicSeadjdist[#1]#2#3{\sdbicase{\SEADJDIST}{#2}{#3}{#100}}%
% pair of south-east adjoint distributors with names
\newcommand{\Seadjdist}{\@ifnextchar[{\basicSeadjdist}{\basicSeadjdist[59]}}%
\let\seadjdisT=\Seadjdist
% NORTH-WEST ARROWS
% \NWAR{n} draws a north-west arrow of length nx100 units
\newcommand{\NWAR}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(\Y,-\Y){\line(-1,1){#1}}%
\put(-\Y,\Y){\nwhead}%
\end{picture}}%
% \NWDIST{n} draws a north-west distributor of length n units
\newcommand{\NWDIST}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(\Y,-\Y){\line(-1,1){#1}}%
\put(-\Y,\Y){\nwhead}%
\truex{400}%
\put(0,0){\circle{\value{x}}}%
\end{picture}}%
% \NWDOTAR{n} draws a north-west dotted arrow of length n units
\newcommand{\NWDOTAR}[1]%
{\truex{100}\truey{212}%
\Y=#1%
\divide\Y by 2%
\NUMBEROFDOTS=#1%
\divide\NUMBEROFDOTS by \value{y}%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(0,0)%
\multiput(\Y,-\Y)(-\value{y},\value{y}){\NUMBEROFDOTS}%
{\circle*{\value{x}}}%
\put(-\Y,\Y){\nwhead}%
\end{picture}}%
% \NWMONO{n} draws a north-west monomorphism of length n units
\newcommand{\NWMONO}[1]{%
\Y=#1%
\divide \Y by 2%
\Truetail%
\bimolength=#1%
\advance\bimolength by -\Truemonotail%
\monolength=\bimolength%
\advance\monolength by -\Y%
\begin{picture}(0,0)%
\put(\monolength,-\monolength){\line(-1,1){\bimolength}}%
\put(\monolength,-\monolength){\nwhead}%
\put(-\Y,\Y){\nwhead}%
\end{picture}}%
% \NWEPI{n} draws a north-west epimorphism of length n units
\newcommand{\NWEPI}[1]{%
\Y=#1%
\divide\Y by 2%
\Truehead%
\bimolength=#1%
\advance\bimolength by -\Trueepihead%
\epilength=\bimolength%
\advance\epilength by -\Y%
\begin{picture}(0,0)%
\put(\Y,-\Y){\line(-1,1){\bimolength}}%
\put(-\epilength,\epilength){\nwhead}%
\put(-\Y,\Y){\nwhead}%
\end{picture}}%
% \NWBIMO{n} draws a north-west bimorphism of length n units
\newcommand{\NWBIMO}[1]{%
\Y=#1%
\divide\Y by 2%
\Truetail\Truehead%
\bimolength=#1%
\advance\bimolength by -\Truemonotail%
\monolength=\bimolength%
\advance\monolength by -\Y%
\advance\bimolength by -\Trueepihead%
\epilength=\bimolength%
\advance\epilength by -\monolength%
\begin{picture}(0,0)%
\put(\monolength,-\monolength){\line(-1,1){\bimolength}}%
\put(\monolength,-\monolength){\nwhead}%
\put(-\epilength,\epilength){\nwhead}%
\put(-\Y,\Y){\nwhead}%
\end{picture}}%
% \NWBIAR{n} draws a pair of north-west arrows of length n units
\newcommand{\NWBIAR}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(\Y,-\Y){\begin{picture}(0,0)%
\truex{247}%
\put(-\value{x},-\value{x}){\line(-1,1){#1}}%
\put(\value{x},\value{x}){\line(-1,1){#1}}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(-\monolength,\epilength){\nwhead}%
\put(-\epilength,\monolength){\nwhead}%
\end{picture}}\end{picture}}%
% \NWBIDIST{n} draws a pair of north-west distributors of length n units
\newcommand{\NWBIDIST}[1]{%
\Y=#1%
\divide\Y by 2%
\truey{400}%
\begin{picture}(0,0)%
\put(\Y,-\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(-\value{x},-\value{x}){\line(-1,1){#1}}%
\put(-\epilength,\monolength){\nwhead}%
\end{picture}}%
\put(\Y,-\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by \value{x}%
\epilength=#1%
\advance\epilength by -\value{x}%
\put(\value{x},\value{x}){\line(-1,1){#1}}%
\put(-\epilength,\monolength){\nwhead}%
\end{picture}}%
\put(-\value{x},-\value{x}){\circle{\value{y}}}%
\put(\value{x},\value{x}){\circle{\value{y}}}%
\end{picture}}%
% \NWADJAR{n} draws a north-west pair of adjoint arrows of length n units
\newcommand{\NWADJAR}[1]{%
\Y=#1%
\divide\Y by 2%
\begin{picture}(0,0)%
\put(\Y,-\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(-\value{x},-\value{x}){\line(-1,1){#1}}%
\put(-\epilength,\monolength){\nwhead}%
\end{picture}}%
\put(-\Y,\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(\value{x},\value{x}){\line(1,-1){#1}}%
\put(\epilength,-\monolength){\sehead}%
\end{picture}}\end{picture}}%
% \NWADJDIST{n} draws a north-west pair of adjoint distributors of length n units
\newcommand{\NWADJDIST}[1]{%
\Y=#1%
\divide\Y by 2%
\truey{400}%
\begin{picture}(0,0)%
\put(\Y,-\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(-\value{x},-\value{x}){\line(-1,1){#1}}%
\put(-\epilength,\monolength){\nwhead}%
\end{picture}}%
\put(-\Y,\Y){\begin{picture}(0,0)%
\truex{247}%
\monolength=#1%
\advance\monolength by -\value{x}%
\epilength=#1%
\advance\epilength by \value{x}%
\put(\value{x},\value{x}){\line(1,-1){#1}}%
\put(\epilength,-\monolength){\sehead}%
\end{picture}}%
\put(-\value{x},-\value{x}){\circle{\value{y}}}%
\put(\value{x},\value{x}){\circle{\value{y}}}%
\end{picture}}%
% All the following commands draw north-west arrows
% north-west arrow of length nx100 units
\def\basicnwar[#1]{\sdcase{\NWAR}{}{}{#100}}%
% north-west arrow
\newcommand{\nwar}{\@ifnextchar[{\basicnwar}{\basicnwar[59]}}%
% north-west arrow with upper name [1] and length nx100 units
\def\basicNwar[#1]#2{\sdcase{\NWAR}{#2}{}{#100}}%
% north-west arrow with upper name
\newcommand{\Nwar}{\@ifnextchar[{\basicNwar}{\basicNwar[59]}}%
% north-west arrow with lower name [1] and length nx100 units
\def\basicnwaR[#1]#2{\sdcase{\NWAR}{}{#2}{#100}}%
% north-west arrow with lower name [1]
\newcommand{\nwaR}{\@ifnextchar[{\basicnwaR}{\basicnwaR[59]}}%
% north-west distributor of length nx100 units
\def\basicnwdist[#1]{\sdcase{\NWDIST}{}{}{#100}}%
% north-west distributor
\newcommand{\nwdist}{\@ifnextchar[{\basicnwdist}{\basicnwdist[59]}}%
% north-west distributor with upper name [1] and length nx100 units
\def\basicNwdist[#1]#2{\sdcase{\NWDIST}{#2}{}{#100}}%
% north-west distributor with upper name
\newcommand{\Nwdist}{\@ifnextchar[{\basicNwdist}{\basicNwdist[59]}}%
% north-west distributor with lower name [1] and length nx100 units
\def\basicnwdisT[#1]#2{\sdcase{\NWDIST}{}{#2}{#100}}%
% north-west distributor with lower name [1]
\newcommand{\nwdisT}{\@ifnextchar[{\basicnwdisT}{\basicnwdisT[59]}}%
% north-west dotted arrow of length nx100 units
\def\basicnwdotar[#1]{\sdcase{\NWDOTAR}{}{}{#100}}%
% north-west dotted arrow
\newcommand{\nwdotar}{\@ifnextchar[{\basicnwdotar}{\basicnwdotar[59]}}%
% north-west dotted arrow with upper name [1] and length nx100 units
\def\basicNwdotar[#1]#2{\sdcase{\NWDOTAR}{#2}{}{#100}}%
% north-west dotted arrow with upper name
\newcommand{\Nwdotar}{\@ifnextchar[{\basicNwdotar}{\basicNwdotar[59]}}%
% north-west dotted arrow with lower name [1] and length nx100 units
\def\basicnwdotaR[#1]#2{\sdcase{\NWDOTAR}{}{#2}{#100}}%
% north-west dotted arrow with lower name [1]
\newcommand{\nwdotaR}{\@ifnextchar[{\basicnwdotaR}{\basicnwdotaR[59]}}%
% north-west monomorphism of length nx100 units
\def\basicnwmono[#1]{\sdcase{\NWMONO}{}{}{#100}}%
% north-west monomorphism
\newcommand{\nwmono}{\@ifnextchar[{\basicnwmono}{\basicnwmono[59]}}%
% north-west monomorphism with upper name [1] and length nx100 units
\def\basicNwmono[#1]#2{\sdcase{\NWMONO}{#2}{}{#100}}%
% north-west monomophism with upper name
\newcommand{\Nwmono}{\@ifnextchar[{\basicNwmono}{\basicNwmono[59]}}%
% north-west monomorphism with lower name [1] and length nx100 units
\def\basicnwmonO[#1]#2{\sdcase{\NWMONO}{}{#2}{#100}}%
% north-west monomorphism with lower name [1]
\newcommand{\nwmonO}{\@ifnextchar[{\basicnwmonO}{\basicnwmonO[59]}}%
% north-west epimorphism of length nx100 units
\def\basicnwepi[#1]{\sdcase{\NWEPI}{}{}{#100}}%
% north-west epimorphism
\newcommand{\nwepi}{\@ifnextchar[{\basicnwepi}{\basicnwepi[59]}}%
% north-west epimorphism with upper name [1] and length nx100 units
\def\basicNwepi[#1]#2{\sdcase{\NWEPI}{#2}{}{#100}}%
% north-west epimorphism with upper name
\newcommand{\Nwepi}{\@ifnextchar[{\basicNwepi}{\basicNwepi[59]}}%
% north-west epimorphism with lower name [1] and length nx100 units
\def\basicnwepI[#1]#2{\sdcase{\NWEPI}{}{#2}{#100}}%
% north-west epimorphism with lower name [1]
\newcommand{\nwepI}{\@ifnextchar[{\basicnwepI}{\basicnwepI[59]}}%
% north-west bimorphism of length nx100 units
\def\basicnwbimo[#1]{\sdcase{\NWBIMO}{}{}{#100}}%
% north-west bimorphism
\newcommand{\nwbimo}{\@ifnextchar[{\basicnwbimo}{\basicnwbimo[59]}}%
% north-west bimorphism with upper name [1] and length nx100 units
\def\basicNwbimo[#1]#2{\sdcase{\NWBIMO}{#2}{}{#100}}%
% north-west bimorphism with upper name
\newcommand{\Nwbimo}{\@ifnextchar[{\basicNwbimo}{\basicNwbimo[59]}}%
% north-west bimorphism with lower name [1] and length nx100 units
\def\basicnwbimO[#1]#2{\sdcase{\NWBIMO}{}{#2}{#100}}%
% north-west bimorphism with lower name [1]
\newcommand{\nwbimO}{\@ifnextchar[{\basicnwbimO}{\basicnwbimO[59]}}%
% north-west isomorphism of length nx100 units
\def\basicnwiso[#1]{\sdcase{\NWAR}{\hspace{-2pt}\cong}{}{#100}}%
% north-west isomorphism
\newcommand{\nwiso}{\@ifnextchar[{\basicnwiso}{\basicnwiso[59]}}%
% north-west isomorphism with upper name [1] and length nx100 units
\def\basicNwiso[#1]#2{\sdcase{\NWAR}{#2}{\cong}{#100}}%
% north-west isomorphism with upper name
\newcommand{\Nwiso}{\@ifnextchar[{\basicNwiso}{\basicNwiso[59]}}%
% north-west isomorphism with lower name [1] and length nx100 units
\def\basicnwisO[#1]#2{\sdcase{\NWAR}{\hspace{-2pt}\cong}{#2}{#100}}%
% north-west isomorphism with lower name [1]
\newcommand{\nwisO}{\@ifnextchar[{\basicnwisO}{\basicnwisO[59]}}%
% north-west equality
\let\nweql=\seeql%
% north-west equality with upper name
\let\Nweql=\Seeql%
% north-west equality with lower name [1]
\let\nweqL=\seeqL%
% pair of north-west arrows of length nx100 units
\def\basicnwbiar[#1]{\sdbicase{\NWBIAR}{}{}{#100}}%
% pair of north-west arrows
\newcommand{\nwbiar}{\@ifnextchar[{\basicnwbiar}{\basicnwbiar[59]}}%
% pair of north-west arrows with names [1][2] and length nx100 units
\def\basicNwbiar[#1]#2#3{\sdbicase{\NWBIAR}{#2}{#3}{#100}}%
% pair of north-west arrows with names
\newcommand{\Nwbiar}{\@ifnextchar[{\basicNwbiar}{\basicNwbiar[59]}}%
\let\nwbiaR=\Nwbiar
% pair of north-west adjoint arrows of length nx100 units
\def\basicnwadjar[#1]{\sdbicase{\NWADJAR}{}{}{#100}}%
% pair of north-west adjoint arrows
\newcommand{\nwadjar}{\@ifnextchar[{\basicnwadjar}{\basicnwadjar[59]}}%
% pair of north-west adjoint arrows with names [1][2] and length nx100 units
\def\basicNwadjar[#1]#2#3{\sdbicase{\NWADJAR}{#2}{#3}{#100}}%
% pair of north-west adjoint arrows with names
\newcommand{\Nwadjar}{\@ifnextchar[{\basicNwadjar}{\basicNwadjar[59]}}%
\let\nwadjaR=\Nwadjar
% pair of north-west distributors of length nx100 units
\def\basicnwbidist[#1]{\sdbicase{\NWBIDIST}{}{}{#100}}%
% pair of north-west distributors
\newcommand{\nwbidist}{\@ifnextchar[{\basicnwbidist}{\basicnwbidist[59]}}%
% pair of north-west distributors with names [1][2] and length nx100 units
\def\basicNwbidist[#1]#2#3{\sdbicase{\NWBIDIST}{#2}{#3}{#100}}%
% pair of north-west distributors with names
\newcommand{\Nwbidist}{\@ifnextchar[{\basicNwbidist}{\basicNwbidist[59]}}%
\let\nwbidisT=\Nwbidist
% pair of north-west adjoint distributors of length nx100 units
\def\basicnwadjdist[#1]{\sdbicase{\NWADJDIST}{}{}{#100}}%
% pair of north-west adjoint distributors
\newcommand{\nwadjdist}{\@ifnextchar[{\basicnwadjdist}{\basicnwadjdist[59]}}%
% pair of north-west adjoint distributors with names [1][2] and length nx100 units
\def\basicNwadjdist[#1]#2#3{\sdbicase{\NWADJDIST}{#2}{#3}{#100}}%
% pair of north-west adjoint distributors with names
\newcommand{\Nwadjdist}{\@ifnextchar[{\basicNwadjdist}{\basicNwadjdist[59]}}%
\let\nwadjdisT=\Nwadjdist
% EAST-NORTH-EAST ARROWS
% The following commands produce east-north-east arrows
% of horizontal extent n units
% \ENEAR{f}{g}{n} draws a east-north-east arrow with names f, g
% and length n units
\newcommand{\ENEAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(-\Y,-\Z){\line(2,1){#3}}%
\put(\Y,\Z){\enehead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \ENEDIST{f}{g}{n} draws a east-north-east distributor
% with names f, g and length n units
\newcommand{\ENEDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(-\Y,-\Z){\line(2,1){#3}}%
\put(\Y,\Z){\enehead}%
\truex{400}%
\put(0,0){\circle{\value{x}}}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \ENEDOTAR{f}{g}{n} draws a north-east dotted arrow
% with names f,g and length n units
\newcommand{\ENEDOTAR}[3]{\testdiagrammode%
\truex{100}\truey{268}\truez{134}%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\NUMBEROFDOTS=#3%
\divide\NUMBEROFDOTS by \value{y}%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(0,0)%
\multiput(-\Y,-\Z)(\value{y},\value{z}){\NUMBEROFDOTS}%
{\circle*{\value{x}}}%
\put(\Y,\Z){\enehead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \ENEMONO{f}{g}{n} draws a east-north-east monomorphism
% with names f,g and length n units
\newcommand{\ENEMONO}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\TrueTail%
\bimolength=#3%
\advance\bimolength by -\TrueMonoTail%
\monolength=\bimolength%
\advance\monolength by -\Y%
\secondmonolength=\monolength%
\divide\secondmonolength by 2%
\begin{picture}(0,0)%
\put(-\monolength,-\secondmonolength){\line(2,1){\bimolength}}%
\put(-\monolength,-\secondmonolength){\enehead}%
\put(\Y,\Z){\enehead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \ENEEPI{f}{g}{n} draws a east-north-east epimorphism
% with names f, g and length n units
\newcommand{\ENEEPI}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\TrueHead%
\bimolength=#3%
\advance\bimolength by -\TrueEpiHead%
\epilength=\bimolength%
\advance\epilength by -\Y%
\secondepilength=\epilength%
\divide\secondepilength by 2%
\begin{picture}(0,0)%
\put(-\Y,-\Z){\line(2,1){\bimolength}}%
\put(\epilength,\secondepilength){\enehead}%
\put(\Y,\Z){\enehead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \ENEBIMO{f}{g}{n} draws a east-north-east bimorphism
% with names f,g and length n units
\newcommand{\ENEBIMO}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\TrueTail\TrueHead%
\bimolength=#3%
\advance\bimolength by -\TrueMonoTail%
\monolength=\bimolength%
\advance\monolength by -\Y%
\advance\bimolength by -\TrueEpiHead%
\epilength=\bimolength%
\advance\epilength by -\monolength%
\secondmonolength=\monolength%
\divide\secondmonolength by 2%
\secondepilength=\epilength%
\divide\secondepilength by 2%
\begin{picture}(0,0)%
\put(-\monolength,-\secondmonolength){\line(2,1){\bimolength}}%
\put(-\monolength,-\secondmonolength){\enehead}%
\put(\epilength,\secondepilength){\enehead}%
\put(\Y,\Z){\enehead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \ENEEQL{f}{g}{n} draws a east-north-east equality
% with names f,g and length n units
\newcommand{\ENEEQL}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(-\Y,-\Z){\begin{picture}(0,0)%
\truex{44}\truey{89}%
\put(-\value{x},\value{y}){\line(2,1){#3}}%
\put(\value{x},-\value{y}){\line(2,1){#3}}%
\end{picture}}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \ENEBIAR{f}{g}{n} draws a pair of east-north-east arrows
% with names f,g and length n units
\newcommand{\ENEBIAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(-\Y,-\Z){\begin{picture}(0,0)%
\truex{156}\truey{313}%
\put(-\value{x},\value{y}){\line(2,1){#3}}%
\put(\value{x},-\value{y}){\line(2,1){#3}}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Y%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Y%
\advance\secondepilength by \value{y}%
\put(\monolength,\secondepilength){\enehead}%
\put(\epilength,\secondmonolength){\enehead}%
\end{picture}}
\truex{300}\truey{1000}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \ENEBIDIST{f}{g}{n} draws a pair of east-north-east distributors
% with names f,g and length n units
\newcommand{\ENEBIDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\truex{156}\truey{313}\truez{400}%
\put(-\Y,-\Z){\begin{picture}(0,0)%
\put(-\value{x},\value{y}){\line(2,1){#3}}%
\put(\value{x},-\value{y}){\line(2,1){#3}}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Y%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Y%
\advance\secondepilength by \value{y}%
\put(\monolength,\secondepilength){\enehead}%
\put(\epilength,\secondmonolength){\enehead}%
\end{picture}}
\put(-\value{x},\value{y}){\circle{\value{z}}}%
\put(\value{x},-\value{y}){\circle{\value{z}}}%
\truex{300}\truey{1000}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \ENEADJAR{f}{g}{n} draws a east-north-east pair of adjoint arrows
% with names f,g and length n units
\newcommand{\ENEADJAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(-\Y,-\Z){\begin{picture}(0,0)%
\truex{156}\truey{313}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Y%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Y%
\advance\secondepilength by \value{y}%
\put(\value{x},-\value{y}){\line(2,1){#3}}%
\put(\epilength,\secondmonolength){\enehead}%
\put(\monolength,\secondepilength){\line(-2,-1){#3}}%
\put(-\value{x},\value{y}){\wswhead}%
\end{picture}}
\truex{300}\truey{1000}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \ENEADJDIST{f}{g}{n} draws a east-north-east pair of adjoint distributors
% with names f,g and length n units
\newcommand{\ENEADJDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\truex{156}\truey{313}\truez{400}%
\put(-\Y,-\Z){\begin{picture}(0,0)%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Y%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Y%
\advance\secondepilength by \value{y}%
\put(\value{x},-\value{y}){\line(2,1){#3}}%
\put(\epilength,\secondmonolength){\enehead}%
\put(\monolength,\secondepilength){\line(-2,-1){#3}}%
\put(-\value{x},\value{y}){\wswhead}%
\end{picture}}
\put(-\value{x},\value{y}){\circle{\value{z}}}%
\put(\value{x},-\value{y}){\circle{\value{z}}}%
\truex{300}\truey{1000}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% The following commands produce east-north-east arrows;
% the default length is 13300 units
% basic east-north-east arrow
\def\basicenear[#1]{\ENEAR{}{}{#100}}%
% east-north-east arrow
\newcommand{\enear}{\@ifnextchar[{\basicenear}{\basicenear[133]}}%
% basic east-north-east arrow with upper name
\def\basicEnear[#1]#2{\ENEAR{#2}{}{#100}}%
% east-north-east arrow with upper name
\newcommand{\Enear}{\@ifnextchar[{\basicEnear}{\basicEnear[133]}}%
% basic east-north-east arrow with lower name
\def\basiceneaR[#1]#2{\ENEAR{}{#2}{#100}}%
% east-north-east arrow with lower name
\newcommand{\eneaR}{\@ifnextchar[{\basiceneaR}{\basiceneaR[133]}}%
% basic east-north-east distributor
\def\basicenedist[#1]{\ENEDIST{}{}{#100}}%
% east-north-east distributor
\newcommand{\enedist}{\@ifnextchar[{\basicenedist}{\basicenedist[133]}}%
% basic east-north-east distributor with upper name
\def\basicEnedist[#1]#2{\ENEDIST{#2}{}{#100}}%
% east-north-east distributor with upper name
\newcommand{\Enedist}{\@ifnextchar[{\basicEnedist}{\basicEnedist[133]}}%
% basic east-north-east distributor with lower name
\def\basicenedisT[#1]#2{\ENEDIST{}{#2}{#100}}%
% east-north-east distributor with lower name
\newcommand{\enedisT}{\@ifnextchar[{\basicenedisT}{\basicenedisT[133]}}%
% basic east-north-east dotted arrow
\def\basicenedotar[#1]{\ENEDOTAR{}{}{#100}}%
% east-north-east dotted arrow
\newcommand{\enedotar}{\@ifnextchar[{\basicenedotar}{\basicenedotar[133]}}%
% basic east-north-east dotted arrow with upper name
\def\basicEnedotar[#1]#2{\ENEDOTAR{#2}{}{#100}}%
% east-north-east dotted arrow with upper name
\newcommand{\Enedotar}{\@ifnextchar[{\basicEnedotar}{\basicEnedotar[133]}}%
% basic east-north-east dotted arrow with lower name
\def\basicenedotaR[#1]#2{\ENEDOTAR{}{#2}{#100}}%
% east-north-east dotted arrow with lower name
\newcommand{\enedotaR}{\@ifnextchar[{\basicenedotaR}{\basicenedotaR[133]}}%
% basic east-north-east monomorphism
\def\basicenemono[#1]{\ENEMONO{}{}{#100}}%
% east-north-east monomorphism
\newcommand{\enemono}{\@ifnextchar[{\basicenemono}{\basicenemono[133]}}%
% basic east-north-east monomorphism with upper name
\def\basicEnemono[#1]#2{\ENEMONO{#2}{}{#100}}%
% east-north-east monomorphism with upper name
\newcommand{\Enemono}{\@ifnextchar[{\basicEnemono}{\basicEnemono[133]}}%
% basic east-north-east monomorphism with lower name
\def\basicenemonO[#1]#2{\ENEMONO{}{#2}{#100}}%
% east-north-east monomorphism with lower name
\newcommand{\enemonO}{\@ifnextchar[{\basicenemonO}{\basicenemonO[133]}}%
% basic east-north-east epimorphism
\def\basiceneepi[#1]{\ENEEPI{}{}{#100}}%
% east-north-east epimorphism
\newcommand{\eneepi}{\@ifnextchar[{\basiceneepi}{\basiceneepi[133]}}%
% basic east-north-east epimorphism with upper name
\def\basicEneepi[#1]#2{\ENEEPI{#2}{}{#100}}%
% east-north-east epimorphism with upper name
\newcommand{\Eneepi}{\@ifnextchar[{\basicEneepi}{\basicEneepi[133]}}%
% basic east-north-east epimorphism with lower name
\def\basiceneepI[#1]#2{\ENEEPI{}{#2}{#100}}%
% east-north-east epimorphism with lower name
\newcommand{\eneepI}{\@ifnextchar[{\basiceneepI}{\basiceneepI[133]}}%
% basic east-north-east bimorphism
\def\basicenebimo[#1]{\ENEBIMO{}{}{#100}}%
% east-north-east bimorphism
\newcommand{\enebimo}{\@ifnextchar[{\basicenebimo}{\basicenebimo[133]}}%
% basic east-north-east bimorphism with upper name
\def\basicEnebimo[#1]#2{\ENEBIMO{#2}{}{#100}}%
% east-north-east bimorphism with upper name
\newcommand{\Enebimo}{\@ifnextchar[{\basicEnebimo}{\basicEnebimo[133]}}%
% basic east-north-east bimorphism with lower name
\def\basicenebimO[#1]#2{\ENEBIMO{}{#2}{#100}}%
% east-north-east bimorphism with lower name
\newcommand{\enebimO}{\@ifnextchar[{\basicenebimO}{\basicenebimO[133]}}%
% basic east-north-east isomorphism
\def\basiceneiso[#1]{\ENEAR{\cong}{}{#100}}%
% east-north-east isomorphism
\newcommand{\eneiso}{\@ifnextchar[{\basiceneiso}{\basiceneiso[133]}}%
% basic east-north-east isomorphism with upper name
\def\basicEneiso[#1]#2{\ENEAR{#2}{\cong}{#100}}%
% east-north-east isomorphism with upper name
\newcommand{\Eneiso}{\@ifnextchar[{\basicEneiso}{\basicEneiso[133]}}%
% basic east-north-east isomorphism with lower name
\def\basiceneisO[#1]#2{\ENEAR{\cong}{#2}{#100}}%
% east-north-east isomorphism with lower name
\newcommand{\eneisO}{\@ifnextchar[{\basiceneisO}{\basiceneisO[133]}}%
% basic east-north-east equality
\def\basiceneeql[#1]{\ENEEQL{}{}{#100}}%
% east-north-east equality
\newcommand{\eneeql}{\@ifnextchar[{\basiceneeql}{\basiceneeql[133]}}%
% basic east-north-east equality with upper name
\def\basicEneeql[#1]#2{\ENEEQL{#2}{}{#100}}%
% east-north-east equality with upper name
\newcommand{\Eneeql}{\@ifnextchar[{\basicEneeql}{\basicEneeql[133]}}%
% basic east-north-east equality with lower name
\def\basiceneeqL[#1]#2{\ENEEQL{}{#2}{#100}}%
% east-north-east equality with lower name
\newcommand{\eneeqL}{\@ifnextchar[{\basiceneeqL}{\basiceneeqL[133]}}%
% basic east-north-east pair of arrows
\def\basicenebiar[#1]{\ENEBIAR{}{}{#100}}%
% east-north-east pair of arrows
\newcommand{\enebiar}{\@ifnextchar[{\basicenebiar}{\basicenebiar[133]}}%
% basic east-north-east pair of arrows with names
\def\basicEnebiar[#1]#2#3{\ENEBIAR{#2}{#3}{#100}}%
% east-north-east pair of arrows with names
\newcommand{\Enebiar}{\@ifnextchar[{\basicEnebiar}{\basicEnebiar[133]}}%
\let\enebiaR=\Enebiar
% basic east-north-east pair of distributors
\def\basicenebidist[#1]{\ENEBIDIST{}{}{#100}}%
% east-north-east pair of distributors
\newcommand{\enebidist}{\@ifnextchar[{\basicenebidist}{\basicenebidist[133]}}%
% basic east-north-east pair of distributors with names
\def\basicEnebidist[#1]#2#3{\ENEBIDIST{#2}{#3}{#100}}%
% east-north-east pair of distributors with names
\newcommand{\Enebidist}{\@ifnextchar[{\basicEnebidist}{\basicEnebidist[133]}}%
\let\enebidisT=\Enebidist
% basic east-north-east pair of adjoint arrows
\def\basiceneadjar[#1]{\ENEADJAR{}{}{#100}}%
% east-north-east pair of adjoint arrows
\newcommand{\eneadjar}{\@ifnextchar[{\basiceneadjar}{\basiceneadjar[133]}}%
% basic east-north-east pair of adjoint arrows with names
\def\basicEneadjar[#1]#2#3{\ENEADJAR{#2}{#3}{#100}}%
% east-north-east pair of adjoint arrows with names
\newcommand{\Eneadjar}{\@ifnextchar[{\basicEneadjar}{\basicEneadjar[133]}}%
\let\eneadjaR=\Eneadjar
% basic east-north-east pair of adjoint distributors
\def\basiceneadjdist[#1]{\ENEADJDIST{}{}{#100}}%
% east-north-east pair of adjoint distributors
\newcommand{\eneadjdist}{\@ifnextchar[{\basiceneadjdist}{\basiceneadjdist[133]}}%
% basic east-north-east pair of adjoint distributors with names
\def\basicEneadjdist[#1]#2#3{\ENEADJDIST{#2}{#3}{#100}}%
% east-north-east pair of adjoint distributors with names
\newcommand{\Eneadjdist}{\@ifnextchar[{\basicEneadjdist}{\basicEneadjdist[133]}}%
\let\eneadjdisT=\Eneadjdist
% EAST-SOUTH-EAST ARROWS
% The following commands produce east-south-east arrows
% of horizontal extent n units
% \ESEAR{f}{g}{n} draws a east-south-east arrow with names f, g
% and length n units
\newcommand{\ESEAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(-\Y,\Z){\line(2,-1){#3}}%
\put(\Y,-\Z){\esehead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \ESEDIST{f}{g}{n} draws a east-south-east distributor
% with names f, g and length n units
\newcommand{\ESEDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(-\Y,\Z){\line(2,-1){#3}}%
\put(\Y,-\Z){\esehead}%
\truex{400}%
\put(0,0){\circle{\value{x}}}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \ESEDOTAR{f}{g}{n} draws a north-east dotted arrow
% with names f,g and length n units
\newcommand{\ESEDOTAR}[3]{\testdiagrammode%
\truex{100}\truey{268}\truez{134}%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\NUMBEROFDOTS=#3%
\divide\NUMBEROFDOTS by \value{y}%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(0,0)%
\multiput(-\Y,\Z)(\value{y},-\value{z}){\NUMBEROFDOTS}%
{\circle*{\value{x}}}%
\put(\Y,-\Z){\esehead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \ESEMONO{f}{g}{n} draws a east-south-east monomorphism
% with names f,g and length n units
\newcommand{\ESEMONO}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\TrueTail%
\bimolength=#3%
\advance\bimolength by -\TrueMonoTail%
\monolength=\bimolength%
\advance\monolength by -\Y%
\secondmonolength=\monolength%
\divide\secondmonolength by 2%
\begin{picture}(0,0)%
\put(-\monolength,\secondmonolength){\line(2,-1){\bimolength}}%
\put(-\monolength,\secondmonolength){\esehead}%
\put(\Y,-\Z){\esehead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \ESEEPI{f}{g}{n} draws a east-south-east epimorphism
% with names f, g and length n units
\newcommand{\ESEEPI}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\TrueHead%
\bimolength=#3%
\advance\bimolength by -\TrueEpiHead%
\epilength=\bimolength%
\advance\epilength by -\Y%
\secondepilength=\epilength%
\divide\secondepilength by 2%
\begin{picture}(0,0)%
\put(-\Y,\Z){\line(2,-1){\bimolength}}%
\put(\epilength,-\secondepilength){\esehead}%
\put(\Y,-\Z){\esehead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \ESEBIMO{f}{g}{n} draws a east-south-east bimorphism
% with names f,g and length n units
\newcommand{\ESEBIMO}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\TrueTail\TrueHead%
\bimolength=#3%
\advance\bimolength by -\TrueMonoTail%
\monolength=\bimolength%
\advance\monolength by -\Y%
\advance\bimolength by -\TrueEpiHead%
\epilength=\bimolength%
\advance\epilength by -\monolength%
\secondmonolength=\monolength%
\divide\secondmonolength by 2%
\secondepilength=\epilength%
\divide\secondepilength by 2%
\begin{picture}(0,0)%
\put(-\monolength,\secondmonolength){\line(2,-1){\bimolength}}%
\put(-\monolength,\secondmonolength){\esehead}%
\put(\epilength,-\secondepilength){\esehead}%
\put(\Y,-\Z){\esehead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \ESEEQL{f}{g}{n} draws a east-south-east equality
% with names f,g and length n units
\newcommand{\ESEEQL}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(-\Y,\Z){\begin{picture}(0,0)%
\truex{44}\truey{89}%
\put(-\value{x},-\value{y}){\line(2,-1){#3}}%
\put(\value{x},\value{y}){\line(2,-1){#3}}%
\end{picture}}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \ESEBIAR{f}{g}{n} draws a pair of east-south-east arrows
% with names f,g and length n units
\newcommand{\ESEBIAR}[3]{%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(-\Y,\Z){\begin{picture}(0,0)%
\truex{156}\truey{313}%
\put(-\value{x},-\value{y}){\line(2,-1){#3}}%
\put(\value{x},\value{y}){\line(2,-1){#3}}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Y%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Y%
\advance\secondepilength by \value{y}%
\put(\monolength,-\secondepilength){\esehead}%
\put(\epilength,-\secondmonolength){\esehead}%
\end{picture}}
\truex{400}\truey{1000}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \ESEBIDIST{f}{g}{n} draws a pair of east-south-east distributors
% with names f,g and length n units
\newcommand{\ESEBIDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\truex{156}\truey{313}\truez{400}%
\put(-\Y,\Z){\begin{picture}(0,0)%
\put(-\value{x},-\value{y}){\line(2,-1){#3}}%
\put(\value{x},\value{y}){\line(2,-1){#3}}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Y%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Y%
\advance\secondepilength by \value{y}%
\put(\monolength,-\secondepilength){\esehead}%
\put(\epilength,-\secondmonolength){\esehead}%
\end{picture}}
\put(\value{x},\value{y}){\circle{\value{z}}}%
\put(-\value{x},-\value{y}){\circle{\value{z}}}%
\truex{400}\truey{1000}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \ESEADJAR{f}{g}{n} draws a east-south-east pair of adjoint arrows
% with names f,g and length n units
\newcommand{\ESEADJAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(-\Y,\Z){\begin{picture}(0,0)%
\truex{156}\truey{313}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Y%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Y%
\advance\secondepilength by \value{y}%
\put(-\value{x},-\value{y}){\line(2,-1){#3}}%
\put(\monolength,-\secondepilength){\esehead}%
\put(\epilength,-\secondmonolength){\line(-2,1){#3}}%
\put(\value{x},\value{y}){\wnwhead}%
\end{picture}}
\truex{400}\truey{1000}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \ESEADJDIST{f}{g}{n} draws a east-south-east pair of adjoint distributors
% with names f,g and length n units
\newcommand{\ESEADJDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\truex{156}\truey{313}\truez{400}%
\put(-\Y,\Z){\begin{picture}(0,0)%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Y%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Y%
\advance\secondepilength by \value{y}%
\put(-\value{x},-\value{y}){\line(2,-1){#3}}%
\put(\monolength,-\secondepilength){\esehead}%
\put(\epilength,-\secondmonolength){\line(-2,1){#3}}%
\put(\value{x},\value{y}){\wnwhead}%
\end{picture}}
\put(\value{x},\value{y}){\circle{\value{z}}}%
\put(-\value{x},-\value{y}){\circle{\value{z}}}%
\truex{400}\truey{1000}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% The following commands produce east-south-east arrows;
% the default length is 13300 units
% basic east-south-east arrow
\def\basicesear[#1]{\ESEAR{}{}{#100}}%
% east-south-east arrow
\newcommand{\esear}{\@ifnextchar[{\basicesear}{\basicesear[133]}}%
% basic east-south-east arrow with upper name
\def\basicEsear[#1]#2{\ESEAR{#2}{}{#100}}%
% east-south-east arrow with upper name
\newcommand{\Esear}{\@ifnextchar[{\basicEsear}{\basicEsear[133]}}%
% basic east-south-east arrow with lower name
\def\basiceseaR[#1]#2{\ESEAR{}{#2}{#100}}%
% east-south-east arrow with lower name
\newcommand{\eseaR}{\@ifnextchar[{\basiceseaR}{\basiceseaR[133]}}%
% basic east-south-east distributor
\def\basicesedist[#1]{\ESEDIST{}{}{#100}}%
% east-south-east distributor
\newcommand{\esedist}{\@ifnextchar[{\basicesedist}{\basicesedist[133]}}%
% basic east-south-east distributor with upper name
\def\basicEsedist[#1]#2{\ESEDIST{#2}{}{#100}}%
% east-south-east distributor with upper name
\newcommand{\Esedist}{\@ifnextchar[{\basicEsedist}{\basicEsedist[133]}}%
% basic east-south-east distributor with lower name
\def\basicesedisT[#1]#2{\ESEDIST{}{#2}{#100}}%
% east-south-east distributor with lower name
\newcommand{\esedisT}{\@ifnextchar[{\basicesedisT}{\basicesedisT[133]}}%
% basic east-south-east dotted arrow
\def\basicesedotar[#1]{\ESEDOTAR{}{}{#100}}%
% east-south-east dotted arrow
\newcommand{\esedotar}{\@ifnextchar[{\basicesedotar}{\basicesedotar[133]}}%
% basic east-south-east dotted arrow with upper name
\def\basicEsedotar[#1]#2{\ESEDOTAR{#2}{}{#100}}%
% east-south-east dotted arrow with upper name
\newcommand{\Esedotar}{\@ifnextchar[{\basicEsedotar}{\basicEsedotar[133]}}%
% basic east-south-east dotted arrow with lower name
\def\basicesedotaR[#1]#2{\ESEDOTAR{}{#2}{#100}}%
% east-south-east dotted arrow with lower name
\newcommand{\esedotaR}{\@ifnextchar[{\basicesedotaR}{\basicesedotaR[133]}}%
% basic east-south-east monomorphism
\def\basicesemono[#1]{\ESEMONO{}{}{#100}}%
% east-south-east monomorphism
\newcommand{\esemono}{\@ifnextchar[{\basicesemono}{\basicesemono[133]}}%
% basic east-south-east monomorphism with upper name
\def\basicEsemono[#1]#2{\ESEMONO{#2}{}{#100}}%
% east-south-east monomorphism with upper name
\newcommand{\Esemono}{\@ifnextchar[{\basicEsemono}{\basicEsemono[133]}}%
% basic east-south-east monomorphism with lower name
\def\basicesemonO[#1]#2{\ESEMONO{}{#2}{#100}}%
% east-south-east monomorphism with lower name
\newcommand{\esemonO}{\@ifnextchar[{\basicesemonO}{\basicesemonO[133]}}%
% basic east-south-east epimorphism
\def\basiceseepi[#1]{\ESEEPI{}{}{#100}}%
% east-south-east epimorphism
\newcommand{\eseepi}{\@ifnextchar[{\basiceseepi}{\basiceseepi[133]}}%
% basic east-south-east epimorphism with upper name
\def\basicEseepi[#1]#2{\ESEEPI{#2}{}{#100}}%
% east-south-east epimorphism with upper name
\newcommand{\Eseepi}{\@ifnextchar[{\basicEseepi}{\basicEseepi[133]}}%
% basic east-south-east epimorphism with lower name
\def\basiceseepI[#1]#2{\ESEEPI{}{#2}{#100}}%
% east-south-east epimorphism with lower name
\newcommand{\eseepI}{\@ifnextchar[{\basiceseepI}{\basiceseepI[133]}}%
% basic east-south-east bimorphism
\def\basicesebimo[#1]{\ESEBIMO{}{}{#100}}%
% east-south-east bimorphism
\newcommand{\esebimo}{\@ifnextchar[{\basicesebimo}{\basicesebimo[133]}}%
% basic east-south-east bimorphism with upper name
\def\basicEsebimo[#1]#2{\ESEBIMO{#2}{}{#100}}%
% east-south-east bimorphism with upper name
\newcommand{\Esebimo}{\@ifnextchar[{\basicEsebimo}{\basicEsebimo[133]}}%
% basic east-south-east bimorphism with lower name
\def\basicesebimO[#1]#2{\ESEBIMO{}{#2}{#100}}%
% east-south-east bimorphism with lower name
\newcommand{\esebimO}{\@ifnextchar[{\basicesebimO}{\basicesebimO[133]}}%
% basic east-south-east isomorphism
\def\basiceseiso[#1]{\ESEAR{\cong}{}{#100}}%
% east-south-east isomorphism
\newcommand{\eseiso}{\@ifnextchar[{\basiceseiso}{\basiceseiso[133]}}%
% basic east-south-east isomorphism with upper name
\def\basicEseiso[#1]#2{\ESEAR{#2}{\cong}{#100}}%
% east-south-east isomorphism with upper name
\newcommand{\Eseiso}{\@ifnextchar[{\basicEseiso}{\basicEseiso[133]}}%
% basic east-south-east isomorphism with lower name
\def\basiceseisO[#1]#2{\ESEAR{\cong}{#2}{#100}}%
% east-south-east isomorphism with lower name
\newcommand{\eseisO}{\@ifnextchar[{\basiceseisO}{\basiceseisO[133]}}%
% basic east-south-east equality
\def\basiceseeql[#1]{\ESEEQL{}{}{#100}}%
% east-south-east equality
\newcommand{\eseeql}{\@ifnextchar[{\basiceseeql}{\basiceseeql[133]}}%
% basic east-south-east equality with upper name
\def\basicEseeql[#1]#2{\ESEEQL{#2}{}{#100}}%
% east-south-east equality with upper name
\newcommand{\Eseeql}{\@ifnextchar[{\basicEseeql}{\basicEseeql[133]}}%
% basic east-south-east equality with lower name
\def\basiceseeqL[#1]#2{\ESEEQL{}{#2}{#100}}%
% east-south-east equality with lower name
\newcommand{\eseeqL}{\@ifnextchar[{\basiceseeqL}{\basiceseeqL[133]}}%
% basic east-south-east pair of arrows
\def\basicesebiar[#1]{\ESEBIAR{}{}{#100}}%
% east-south-east pair of arrows
\newcommand{\esebiar}{\@ifnextchar[{\basicesebiar}{\basicesebiar[133]}}%
% basic east-south-east pair of arrows with names
\def\basicEsebiar[#1]#2#3{\ESEBIAR{#2}{#3}{#100}}%
% east-south-east pair of arrows with names
\newcommand{\Esebiar}{\@ifnextchar[{\basicEsebiar}{\basicEsebiar[133]}}%
\let\esebiaR=\Esebiar
% basic east-south-east pair of distributors
\def\basicesebidist[#1]{\ESEBIDIST{}{}{#100}}%
% east-south-east pair of distributors
\newcommand{\esebidist}{\@ifnextchar[{\basicesebidist}{\basicesebidist[133]}}%
% basic east-south-east pair of distributors with names
\def\basicEsebidist[#1]#2#3{\ESEBIDIST{#2}{#3}{#100}}%
% east-south-east pair of distributors with names
\newcommand{\Esebidist}{\@ifnextchar[{\basicEsebidist}{\basicEsebidist[133]}}%
\let\esebidisT=\Esebidist
% basic east-south-east pair of adjoint arrows
\def\basiceseadjar[#1]{\ESEADJAR{}{}{#100}}%
% east-south-east pair of adjoint arrows
\newcommand{\eseadjar}{\@ifnextchar[{\basiceseadjar}{\basiceseadjar[133]}}%
% basic east-south-east pair of adjoint arrows with names
\def\basicEseadjar[#1]#2#3{\ESEADJAR{#2}{#3}{#100}}%
% east-south-east pair of adjoint arrows with names
\newcommand{\Eseadjar}{\@ifnextchar[{\basicEseadjar}{\basicEseadjar[133]}}%
\let\eseadjaR=\Eseadjar
% basic east-south-east pair of adjoint distributors
\def\basiceseadjdist[#1]{\ESEADJDIST{}{}{#100}}%
% east-south-east pair of adjoint distributors
\newcommand{\eseadjdist}{\@ifnextchar[{\basiceseadjdist}{\basiceseadjdist[133]}}%
% basic east-south-east pair of adjoint distributors with names
\def\basicEseadjdist[#1]#2#3{\ESEADJDIST{#2}{#3}{#100}}%
% east-south-east pair of adjoint distributors with names
\newcommand{\Eseadjdist}{\@ifnextchar[{\basicEseadjdist}{\basicEseadjdist[133]}}%
\let\eseadjdisT=\Eseadjdist
% WEST-SOUTH-WEST ARROWS
% The following commands produce west-south-west arrows
% of horizontal extent n units
% \WSWAR{f}{g}{n} draws a west-south-west arrow with names f, g
% and length n units
\newcommand{\WSWAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(\Y,\Z){\line(-2,-1){#3}}%
\put(-\Y,-\Z){\wswhead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \WSWDIST{f}{g}{n} draws a west-south-west distributor
% with names f, g and length n units
\newcommand{\WSWDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(\Y,\Z){\line(-2,-1){#3}}%
\put(-\Y,-\Z){\wswhead}%
\truex{400}%
\put(0,0){\circle{\value{x}}}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \WSWDOTAR{f}{g}{n} draws a north-east dotted arrow
% with names f,g and length n units
\newcommand{\WSWDOTAR}[3]{\testdiagrammode%
\truex{100}\truey{268}\truez{134}%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\NUMBEROFDOTS=#3%
\divide\NUMBEROFDOTS by \value{y}%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(0,0)%
\multiput(\Y,\Z)(-\value{y},-\value{z}){\NUMBEROFDOTS}%
{\circle*{\value{x}}}%
\put(-\Y,-\Z){\wswhead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \WSWMONO{f}{g}{n} draws a west-south-west monomorphism
% with names f,g and length n units
\newcommand{\WSWMONO}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\TrueTail%
\bimolength=#3%
\advance\bimolength by -\TrueMonoTail%
\monolength=\bimolength%
\advance\monolength by -\Y%
\secondmonolength=\monolength%
\divide\secondmonolength by 2%
\begin{picture}(0,0)%
\put(\monolength,\secondmonolength){\line(-2,-1){\bimolength}}%
\put(\monolength,\secondmonolength){\wswhead}%
\put(-\Y,-\Z){\wswhead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \WSWEPI{f}{g}{n} draws a west-south-west epimorphism
% with names f, g and length n units
\newcommand{\WSWEPI}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\TrueHead%
\bimolength=#3%
\advance\bimolength by -\TrueEpiHead%
\epilength=\bimolength%
\advance\epilength by -\Y%
\secondepilength=\epilength%
\divide\secondepilength by 2%
\begin{picture}(0,0)%
\put(\Y,\Z){\line(-2,-1){\bimolength}}%
\put(-\epilength,-\secondepilength){\wswhead}%
\put(-\Y,-\Z){\wswhead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \WSWBIMO{f}{g}{n} draws a west-south-west bimorphism
% with names f,g and length n units
\newcommand{\WSWBIMO}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\TrueTail\TrueHead%
\bimolength=#3%
\advance\bimolength by -\TrueMonoTail%
\monolength=\bimolength%
\advance\monolength by -\Y%
\advance\bimolength by -\TrueEpiHead%
\epilength=\bimolength%
\advance\epilength by -\monolength%
\secondmonolength=\monolength%
\divide\secondmonolength by 2%
\secondepilength=\epilength%
\divide\secondepilength by 2%
\begin{picture}(0,0)%
\put(\monolength,\secondmonolength){\line(-2,-1){\bimolength}}%
\put(\monolength,\secondmonolength){\wswhead}%
\put(-\epilength,-\secondepilength){\wswhead}%
\put(-\Y,-\Z){\wswhead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \WSWBIAR{f}{g}{n} draws a pair of west-south-west arrows
% with names f,g and length n units
\newcommand{\WSWBIAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(\Y,\Z){\begin{picture}(0,0)%
\truex{156}\truey{313}%
\put(-\value{x},\value{y}){\line(-2,-1){#3}}%
\put(\value{x},-\value{y}){\line(-2,-1){#3}}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Y%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Y%
\advance\secondepilength by \value{y}%
\put(-\monolength,-\secondepilength){\wswhead}%
\put(-\epilength,-\secondmonolength){\wswhead}%
\end{picture}}
\truex{300}\truey{1000}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \WSWBIDIST{f}{g}{n} draws a pair of west-south-west distributors
% with names f,g and length n units
\newcommand{\WSWBIDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\truex{156}\truey{313}\truez{400}%
\put(\Y,\Z){\begin{picture}(0,0)%
\put(-\value{x},\value{y}){\line(-2,-1){#3}}%
\put(\value{x},-\value{y}){\line(-2,-1){#3}}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Y%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Y%
\advance\secondepilength by \value{y}%
\put(-\monolength,-\secondepilength){\wswhead}%
\put(-\epilength,-\secondmonolength){\wswhead}%
\end{picture}}
\put(-\value{x},\value{y}){\circle{\value{z}}}%
\put(\value{x},-\value{y}){\circle{\value{z}}}%
\truex{300}\truey{1000}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \WSWADJAR{f}{g}{n} draws a west-south-west pair of adjoint arrows
% with names f,g and length n units
\newcommand{\WSWADJAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(\Y,\Z){\begin{picture}(0,0)%
\truex{156}\truey{313}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Y%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Y%
\advance\secondepilength by \value{y}%
\put(\value{x},-\value{y}){\line(-2,-1){#3}}%
\put(-\monolength,-\secondepilength){\wswhead}%
\put(-\epilength,-\secondmonolength){\line(2,1){#3}}%
\put(-\value{x},\value{y}){\enehead}%
\end{picture}}
\truex{300}\truey{1000}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \WSWADJDIST{f}{g}{n} draws a west-south-west pair of adjoint distributors
% with names f,g and length n units
\newcommand{\WSWADJDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\truex{156}\truey{313}\truez{400}%
\put(\Y,\Z){\begin{picture}(0,0)%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Y%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Y%
\advance\secondepilength by \value{y}%
\put(\value{x},-\value{y}){\line(-2,-1){#3}}%
\put(-\monolength,-\secondepilength){\wswhead}%
\put(-\epilength,-\secondmonolength){\line(2,1){#3}}%
\put(-\value{x},\value{y}){\enehead}%
\end{picture}}
\put(-\value{x},\value{y}){\circle{\value{z}}}%
\put(\value{x},-\value{y}){\circle{\value{z}}}%
\truex{300}\truey{1000}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% The following commands produce west-south-west arrows;
% the default length is 13300 units
% basic west-south-west arrow
\def\basicwswar[#1]{\WSWAR{}{}{#100}}%
% west-south-west arrow
\newcommand{\wswar}{\@ifnextchar[{\basicwswar}{\basicwswar[133]}}%
% basic west-south-west arrow with upper name
\def\basicWswar[#1]#2{\WSWAR{#2}{}{#100}}%
% west-south-west arrow with upper name
\newcommand{\Wswar}{\@ifnextchar[{\basicWswar}{\basicWswar[133]}}%
% basic west-south-west arrow with lower name
\def\basicwswaR[#1]#2{\WSWAR{}{#2}{#100}}%
% west-south-west arrow with lower name
\newcommand{\wswaR}{\@ifnextchar[{\basicwswaR}{\basicwswaR[133]}}%
% basic west-south-west distributor
\def\basicwswdist[#1]{\WSWDIST{}{}{#100}}%
% west-south-west distributor
\newcommand{\wswdist}{\@ifnextchar[{\basicwswdist}{\basicwswdist[133]}}%
% basic west-south-west distributor with upper name
\def\basicWswdist[#1]#2{\WSWDIST{#2}{}{#100}}%
% west-south-west distributor with upper name
\newcommand{\Wswdist}{\@ifnextchar[{\basicWswdist}{\basicWswdist[133]}}%
% basic west-south-west distributor with lower name
\def\basicwswdisT[#1]#2{\WSWDIST{}{#2}{#100}}%
% west-south-west distributor with lower name
\newcommand{\wswdisT}{\@ifnextchar[{\basicwswdisT}{\basicwswdisT[133]}}%
% basic west-south-west dotted arrow
\def\basicwswdotar[#1]{\WSWDOTAR{}{}{#100}}%
% west-south-west dotted arrow
\newcommand{\wswdotar}{\@ifnextchar[{\basicwswdotar}{\basicwswdotar[133]}}%
% basic west-south-west dotted arrow with upper name
\def\basicWswdotar[#1]#2{\WSWDOTAR{#2}{}{#100}}%
% west-south-west dotted arrow with upper name
\newcommand{\Wswdotar}{\@ifnextchar[{\basicWswdotar}{\basicWswdotar[133]}}%
% basic west-south-west dotted arrow with lower name
\def\basicwswdotaR[#1]#2{\WSWDOTAR{}{#2}{#100}}%
% west-south-west dotted arrow with lower name
\newcommand{\wswdotaR}{\@ifnextchar[{\basicwswdotaR}{\basicwswdotaR[133]}}%
% basic west-south-west monomorphism
\def\basicwswmono[#1]{\WSWMONO{}{}{#100}}%
% west-south-west monomorphism
\newcommand{\wswmono}{\@ifnextchar[{\basicwswmono}{\basicwswmono[133]}}%
% basic west-south-west monomorphism with upper name
\def\basicWswmono[#1]#2{\WSWMONO{#2}{}{#100}}%
% west-south-west monomorphism with upper name
\newcommand{\Wswmono}{\@ifnextchar[{\basicWswmono}{\basicWswmono[133]}}%
% basic west-south-west monomorphism with lower name
\def\basicwswmonO[#1]#2{\WSWMONO{}{#2}{#100}}%
% west-south-west monomorphism with lower name
\newcommand{\wswmonO}{\@ifnextchar[{\basicwswmonO}{\basicwswmonO[133]}}%
% basic west-south-west epimorphism
\def\basicwswepi[#1]{\WSWEPI{}{}{#100}}%
% west-south-west epimorphism
\newcommand{\wswepi}{\@ifnextchar[{\basicwswepi}{\basicwswepi[133]}}%
% basic west-south-west epimorphism with upper name
\def\basicWswepi[#1]#2{\WSWEPI{#2}{}{#100}}%
% west-south-west epimorphism with upper name
\newcommand{\Wswepi}{\@ifnextchar[{\basicWswepi}{\basicWswepi[133]}}%
% basic west-south-west epimorphism with lower name
\def\basicwswepI[#1]#2{\WSWEPI{}{#2}{#100}}%
% west-south-west epimorphism with lower name
\newcommand{\wswepI}{\@ifnextchar[{\basicwswepI}{\basicwswepI[133]}}%
% basic west-south-west bimorphism
\def\basicwswbimo[#1]{\WSWBIMO{}{}{#100}}%
% west-south-west bimorphism
\newcommand{\wswbimo}{\@ifnextchar[{\basicwswbimo}{\basicwswbimo[133]}}%
% basic west-south-west bimorphism with upper name
\def\basicWswbimo[#1]#2{\WSWBIMO{#2}{}{#100}}%
% west-south-west bimorphism with upper name
\newcommand{\Wswbimo}{\@ifnextchar[{\basicWswbimo}{\basicWswbimo[133]}}%
% basic west-south-west bimorphism with lower name
\def\basicwswbimO[#1]#2{\WSWBIMO{}{#2}{#100}}%
% west-south-west bimorphism with lower name
\newcommand{\wswbimO}{\@ifnextchar[{\basicwswbimO}{\basicwswbimO[133]}}%
% basic west-south-west isomorphism
\def\basicwswiso[#1]{\WSWAR{\cong}{}{#100}}%
% west-south-west isomorphism
\newcommand{\wswiso}{\@ifnextchar[{\basicwswiso}{\basicwswiso[133]}}%
% basic west-south-west isomorphism with upper name
\def\basicWswiso[#1]#2{\WSWAR{#2}{\cong}{#100}}%
% west-south-west isomorphism with upper name
\newcommand{\Wswiso}{\@ifnextchar[{\basicWswiso}{\basicWswiso[133]}}%
% basic west-south-west isomorphism with lower name
\def\basicwswisO[#1]#2{\WSWAR{\cong}{#2}{#100}}%
% west-south-west isomorphism with lower name
\newcommand{\wswisO}{\@ifnextchar[{\basicwswisO}{\basicwswisO[133]}}%
% west-south-west equality
\let\wsweql=\eneeql%
% west-south-west equality with upper name
\let\Wsweql=\Eneeql%
% west-south-west equality with lower name
\let\wsweqL=\eneeqL%
% basic west-south-west pair of arrows
\def\basicwswbiar[#1]{\WSWBIAR{}{}{#100}}%
% west-south-west pair of arrows
\newcommand{\wswbiar}{\@ifnextchar[{\basicwswbiar}{\basicwswbiar[133]}}%
% basic west-south-west pair of arrows with names
\def\basicWswbiar[#1]#2#3{\WSWBIAR{#2}{#3}{#100}}%
% west-south-west pair of arrows with names
\newcommand{\Wswbiar}{\@ifnextchar[{\basicWswbiar}{\basicWswbiar[133]}}%
\let\wswbiaR=\Wswbiar
% basic west-south-west pair of distributors
\def\basicwswbidist[#1]{\WSWBIDIST{}{}{#100}}%
% west-south-west pair of distributors
\newcommand{\wswbidist}{\@ifnextchar[{\basicwswbidist}{\basicwswbidist[133]}}%
% basic west-south-west pair of distributors with names
\def\basicWswbidist[#1]#2#3{\WSWBIDIST{#2}{#3}{#100}}%
% west-south-west pair of distributors with names
\newcommand{\Wswbidist}{\@ifnextchar[{\basicWswbidist}{\basicWswbidist[133]}}%
\let\wswbidisT=\Wswbidist
% basic west-south-west pair of adjoint arrows
\def\basicwswadjar[#1]{\WSWADJAR{}{}{#100}}%
% west-south-west pair of adjoint arrows
\newcommand{\wswadjar}{\@ifnextchar[{\basicwswadjar}{\basicwswadjar[133]}}%
% basic west-south-west pair of adjoint arrows with names
\def\basicWswadjar[#1]#2#3{\WSWADJAR{#2}{#3}{#100}}%
% west-south-west pair of adjoint arrows with names
\newcommand{\Wswadjar}{\@ifnextchar[{\basicWswadjar}{\basicWswadjar[133]}}%
\let\wswadjaR=\Wswadjar
% basic west-south-west pair of adjoint distributors
\def\basicwswadjdist[#1]{\WSWADJDIST{}{}{#100}}%
% west-south-west pair of adjoint distributors
\newcommand{\wswadjdist}{\@ifnextchar[{\basicwswadjdist}{\basicwswadjdist[133]}}%
% basic west-south-west pair of adjoint distributors with names
\def\basicWswadjdist[#1]#2#3{\WSWADJDIST{#2}{#3}{#100}}%
% west-south-west pair of adjoint distributors with names
\newcommand{\Wswadjdist}{\@ifnextchar[{\basicWswadjdist}{\basicWswadjdist[133]}}%
\let\wswadjdisT=\Wswadjdist
% WEST-NORTH-WEST ARROWS
% The following commands produce west-north-west arrows
% of horizontal extent n units
% \WNWAR{f}{g}{n} draws a west-north-west arrow with names f, g
% and length n units
\newcommand{\WNWAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(\Y,-\Z){\line(-2,1){#3}}%
\put(-\Y,\Z){\wnwhead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \WNWDIST{f}{g}{n} draws a west-north-west distributor
% with names f, g and length n units
\newcommand{\WNWDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(\Y,-\Z){\line(-2,1){#3}}%
\put(-\Y,\Z){\wnwhead}%
\truex{400}%
\put(0,0){\circle{\value{x}}}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \WNWDOTAR{f}{g}{n} draws a north-east dotted arrow
% with names f,g and length n units
\newcommand{\WNWDOTAR}[3]{\testdiagrammode%
\truex{100}\truey{268}\truez{134}%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\NUMBEROFDOTS=#3%
\divide\NUMBEROFDOTS by \value{y}%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(0,0)%
\multiput(\Y,-\Z)(-\value{y},\value{z}){\NUMBEROFDOTS}%
{\circle*{\value{x}}}%
\put(-\Y,\Z){\wnwhead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \WNWMONO{f}{g}{n} draws a west-north-west monomorphism
% with names f,g and length n units
\newcommand{\WNWMONO}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\TrueTail%
\bimolength=#3%
\advance\bimolength by -\TrueMonoTail%
\monolength=\bimolength%
\advance\monolength by -\Y%
\secondmonolength=\monolength%
\divide\secondmonolength by 2%
\begin{picture}(0,0)%
\put(\monolength,-\secondmonolength){\line(-2,1){\bimolength}}%
\put(\monolength,-\secondmonolength){\wnwhead}%
\put(-\Y,\Z){\wnwhead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \WNWEPI{f}{g}{n} draws a west-north-west epimorphism
% with names f, g and length n units
\newcommand{\WNWEPI}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\TrueHead%
\bimolength=#3%
\advance\bimolength by -\TrueEpiHead%
\epilength=\bimolength%
\advance\epilength by -\Y%
\secondepilength=\epilength%
\divide\secondepilength by 2%
\begin{picture}(0,0)%
\put(\Y,-\Z){\line(-2,1){\bimolength}}%
\put(-\epilength,\secondepilength){\wnwhead}%
\put(-\Y,\Z){\wnwhead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \WNWBIMO{f}{g}{n} draws a west-north-west bimorphism
% with names f,g and length n units
\newcommand{\WNWBIMO}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\TrueTail\TrueHead%
\bimolength=#3%
\advance\bimolength by -\TrueMonoTail%
\monolength=\bimolength%
\advance\monolength by -\Y%
\advance\bimolength by -\TrueEpiHead%
\epilength=\bimolength%
\advance\epilength by -\monolength%
\secondmonolength=\monolength%
\divide\secondmonolength by 2%
\secondepilength=\epilength%
\divide\secondepilength by 2%
\begin{picture}(0,0)%
\put(\monolength,-\secondmonolength){\line(-2,1){\bimolength}}%
\put(\monolength,-\secondmonolength){\wnwhead}%
\put(-\epilength,\secondepilength){\wnwhead}%
\put(-\Y,\Z){\wnwhead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \WNWBIAR{f}{g}{n} draws a pair of west-north-west arrows
% with names f,g and length n units
\newcommand{\WNWBIAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(\Y,-\Z){\begin{picture}(0,0)%
\truex{156}\truey{313}%
\put(-\value{x},-\value{y}){\line(-2,1){#3}}%
\put(\value{x},\value{y}){\line(-2,1){#3}}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Y%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Y%
\advance\secondepilength by \value{y}%
\put(-\monolength,\secondepilength){\wnwhead}%
\put(-\epilength,\secondmonolength){\wnwhead}%
\end{picture}}
\truex{400}\truey{1000}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \WNWBIDIST{f}{g}{n} draws a pair of west-north-west distributors
% with names f,g and length n units
\newcommand{\WNWBIDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\truex{156}\truey{313}\truez{400}%
\put(\Y,-\Z){\begin{picture}(0,0)%
\put(-\value{x},-\value{y}){\line(-2,1){#3}}%
\put(\value{x},\value{y}){\line(-2,1){#3}}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Y%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Y%
\advance\secondepilength by \value{y}%
\put(-\monolength,\secondepilength){\wnwhead}%
\put(-\epilength,\secondmonolength){\wnwhead}%
\end{picture}}
\put(\value{x},\value{y}){\circle{\value{z}}}%
\put(-\value{x},-\value{y}){\circle{\value{z}}}%
\truex{400}\truey{1000}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \WNWADJAR{f}{g}{n} draws a west-north-west pair of adjoint arrows
% with names f,g and length n units
\newcommand{\WNWADJAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(\Y,-\Z){\begin{picture}(0,0)%
\truex{156}\truey{313}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Y%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Y%
\advance\secondepilength by \value{y}%
\put(-\value{x},-\value{y}){\line(-2,1){#3}}%
\put(-\epilength,\secondmonolength){\wnwhead}%
\put(-\monolength,\secondepilength){\line(2,-1){#3}}%
\put(\value{x},\value{y}){\esehead}%
\end{picture}}
\truex{400}\truey{1000}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \WNWADJDIST{f}{g}{n} draws a west-north-west pair of adjoint distributors
% with names f,g and length n units
\newcommand{\WNWADJDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=\Y%
\divide\Z by 2%
\begin{picture}(0,0)%
\truex{156}\truey{313}\truez{400}%
\put(\Y,-\Z){\begin{picture}(0,0)%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Y%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Y%
\advance\secondepilength by \value{y}%
\put(-\value{x},-\value{y}){\line(-2,1){#3}}%
\put(-\epilength,\secondmonolength){\wnwhead}%
\put(-\monolength,\secondepilength){\line(2,-1){#3}}%
\put(\value{x},\value{y}){\esehead}%
\end{picture}}
\put(\value{x},\value{y}){\circle{\value{z}}}%
\put(-\value{x},-\value{y}){\circle{\value{z}}}%
\truex{400}\truey{1000}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% The following commands produce west-north-west arrows;
% the default length is 13300 units
% basic west-north-west arrow
\def\basicwnwar[#1]{\WNWAR{}{}{#100}}%
% west-north-west arrow
\newcommand{\wnwar}{\@ifnextchar[{\basicwnwar}{\basicwnwar[133]}}%
% basic west-north-west arrow with upper name
\def\basicWnwar[#1]#2{\WNWAR{#2}{}{#100}}%
% west-north-west arrow with upper name
\newcommand{\Wnwar}{\@ifnextchar[{\basicWnwar}{\basicWnwar[133]}}%
% basic west-north-west arrow with lower name
\def\basicwnwaR[#1]#2{\WNWAR{}{#2}{#100}}%
% west-north-west arrow with lower name
\newcommand{\wnwaR}{\@ifnextchar[{\basicwnwaR}{\basicwnwaR[133]}}%
% basic west-north-west distributor
\def\basicwnwdist[#1]{\WNWDIST{}{}{#100}}%
% west-north-west distributor
\newcommand{\wnwdist}{\@ifnextchar[{\basicwnwdist}{\basicwnwdist[133]}}%
% basic west-north-west distributor with upper name
\def\basicWnwdist[#1]#2{\WNWDIST{#2}{}{#100}}%
% west-north-west distributor with upper name
\newcommand{\Wnwdist}{\@ifnextchar[{\basicWnwdist}{\basicWnwdist[133]}}%
% basic west-north-west distributor with lower name
\def\basicwnwdisT[#1]#2{\WNWDIST{}{#2}{#100}}%
% west-north-west distributor with lower name
\newcommand{\wnwdisT}{\@ifnextchar[{\basicwnwdisT}{\basicwnwdisT[133]}}%
% basic west-north-west dotted arrow
\def\basicwnwdotar[#1]{\WNWDOTAR{}{}{#100}}%
% west-north-west dotted arrow
\newcommand{\wnwdotar}{\@ifnextchar[{\basicwnwdotar}{\basicwnwdotar[133]}}%
% basic west-north-west dotted arrow with upper name
\def\basicWnwdotar[#1]#2{\WNWDOTAR{#2}{}{#100}}%
% west-north-west dotted arrow with upper name
\newcommand{\Wnwdotar}{\@ifnextchar[{\basicWnwdotar}{\basicWnwdotar[133]}}%
% basic west-north-west dotted arrow with lower name
\def\basicwnwdotaR[#1]#2{\WNWDOTAR{}{#2}{#100}}%
% west-north-west dotted arrow with lower name
\newcommand{\wnwdotaR}{\@ifnextchar[{\basicwnwdotaR}{\basicwnwdotaR[133]}}%
% basic west-north-west monomorphism
\def\basicwnwmono[#1]{\WNWMONO{}{}{#100}}%
% west-north-west monomorphism
\newcommand{\wnwmono}{\@ifnextchar[{\basicwnwmono}{\basicwnwmono[133]}}%
% basic west-north-west monomorphism with upper name
\def\basicWnwmono[#1]#2{\WNWMONO{#2}{}{#100}}%
% west-north-west monomorphism with upper name
\newcommand{\Wnwmono}{\@ifnextchar[{\basicWnwmono}{\basicWnwmono[133]}}%
% basic west-north-west monomorphism with lower name
\def\basicwnwmonO[#1]#2{\WNWMONO{}{#2}{#100}}%
% west-north-west monomorphism with lower name
\newcommand{\wnwmonO}{\@ifnextchar[{\basicwnwmonO}{\basicwnwmonO[133]}}%
% basic west-north-west epimorphism
\def\basicwnwepi[#1]{\WNWEPI{}{}{#100}}%
% west-north-west epimorphism
\newcommand{\wnwepi}{\@ifnextchar[{\basicwnwepi}{\basicwnwepi[133]}}%
% basic west-north-west epimorphism with upper name
\def\basicWnwepi[#1]#2{\WNWEPI{#2}{}{#100}}%
% west-north-west epimorphism with upper name
\newcommand{\Wnwepi}{\@ifnextchar[{\basicWnwepi}{\basicWnwepi[133]}}%
% basic west-north-west epimorphism with lower name
\def\basicwnwepI[#1]#2{\WNWEPI{}{#2}{#100}}%
% west-north-west epimorphism with lower name
\newcommand{\wnwepI}{\@ifnextchar[{\basicwnwepI}{\basicwnwepI[133]}}%
% basic west-north-west bimorphism
\def\basicwnwbimo[#1]{\WNWBIMO{}{}{#100}}%
% west-north-west bimorphism
\newcommand{\wnwbimo}{\@ifnextchar[{\basicwnwbimo}{\basicwnwbimo[133]}}%
% basic west-north-west bimorphism with upper name
\def\basicWnwbimo[#1]#2{\WNWBIMO{#2}{}{#100}}%
% west-north-west bimorphism with upper name
\newcommand{\Wnwbimo}{\@ifnextchar[{\basicWnwbimo}{\basicWnwbimo[133]}}%
% basic west-north-west bimorphism with lower name
\def\basicwnwbimO[#1]#2{\WNWBIMO{}{#2}{#100}}%
% west-north-west bimorphism with lower name
\newcommand{\wnwbimO}{\@ifnextchar[{\basicwnwbimO}{\basicwnwbimO[133]}}%
% basic west-north-west isomorphism
\def\basicwnwiso[#1]{\WNWAR{\cong}{}{#100}}%
% west-north-west isomorphism
\newcommand{\wnwiso}{\@ifnextchar[{\basicwnwiso}{\basicwnwiso[133]}}%
% basic west-north-west isomorphism with upper name
\def\basicWnwiso[#1]#2{\WNWAR{#2}{\cong}{#100}}%
% west-north-west isomorphism with upper name
\newcommand{\Wnwiso}{\@ifnextchar[{\basicWnwiso}{\basicWnwiso[133]}}%
% basic west-north-west isomorphism with lower name
\def\basicwnwisO[#1]#2{\WNWAR{\cong}{#2}{#100}}%
% west-north-west isomorphism with lower name
\newcommand{\wnwisO}{\@ifnextchar[{\basicwnwisO}{\basicwnwisO[133]}}%
% west-north-west equality
\let\wnweql=\eseeql%
% west-north-west equality with upper name
\let\Wnweql=\Eseeql%
% west-north-west equality with lower name
\let\wnweqL=\eseeqL%
% basic west-north-west pair of arrows
\def\basicwnwbiar[#1]{\WNWBIAR{}{}{#100}}%
% west-north-west pair of arrows
\newcommand{\wnwbiar}{\@ifnextchar[{\basicwnwbiar}{\basicwnwbiar[133]}}%
% basic west-north-west pair of arrows with names
\def\basicWnwbiar[#1]#2#3{\WNWBIAR{#2}{#3}{#100}}%
% west-north-west pair of arrows with names
\newcommand{\Wnwbiar}{\@ifnextchar[{\basicWnwbiar}{\basicWnwbiar[133]}}%
\let\wnwbiaR=\Wnwbiar
% basic west-north-west pair of distributors
\def\basicwnwbidist[#1]{\WNWBIDIST{}{}{#100}}%
% west-north-west pair of distributors
\newcommand{\wnwbidist}{\@ifnextchar[{\basicwnwbidist}{\basicwnwbidist[133]}}%
% basic west-north-west pair of distributors with names
\def\basicWnwbidist[#1]#2#3{\WNWBIDIST{#2}{#3}{#100}}%
% west-north-west pair of distributors with names
\newcommand{\Wnwbidist}{\@ifnextchar[{\basicWnwbidist}{\basicWnwbidist[133]}}%
\let\wnwbidisT=\Wnwbidist
% basic west-north-west pair of adjoint arrows
\def\basicwnwadjar[#1]{\WNWADJAR{}{}{#100}}%
% west-north-west pair of adjoint arrows
\newcommand{\wnwadjar}{\@ifnextchar[{\basicwnwadjar}{\basicwnwadjar[133]}}%
% basic west-north-west pair of adjoint arrows with names
\def\basicWnwadjar[#1]#2#3{\WNWADJAR{#2}{#3}{#100}}%
% west-north-west pair of adjoint arrows with names
\newcommand{\Wnwadjar}{\@ifnextchar[{\basicWnwadjar}{\basicWnwadjar[133]}}%
\let\wnwadjaR=\Wnwadjar
% basic west-north-west pair of adjoint distributors
\def\basicwnwadjdist[#1]{\WNWADJDIST{}{}{#100}}%
% west-north-west pair of adjoint distributors
\newcommand{\wnwadjdist}{\@ifnextchar[{\basicwnwadjdist}{\basicwnwadjdist[133]}}%
% basic west-north-west pair of adjoint distributors with names
\def\basicWnwadjdist[#1]#2#3{\WNWADJDIST{#2}{#3}{#100}}%
% west-north-west pair of adjoint distributors with names
\newcommand{\Wnwadjdist}{\@ifnextchar[{\basicWnwadjdist}{\basicWnwadjdist[133]}}%
\let\wnwadjdisT=\Wnwadjdist
% NORTH-NORTH-EAST ARROWS
% The following commands produce north-north-east arrows
% of horizontal extent n units
% \NNEAR{f}{g}{n} draws a north-north-east arrow with names f, g
% and length n units
\newcommand{\NNEAR}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(-\Z,-#3){\line(1,2){#3}}%
\put(\Z,#3){\nnehead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \NNEDIST{f}{g}{n} draws a north-north-east distributor
% with names f, g and length n units
\newcommand{\NNEDIST}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(-\Z,-#3){\line(1,2){#3}}%
\put(\Z,#3){\nnehead}%
\truex{400}%
\put(0,0){\circle{\value{x}}}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \NNEDOTAR{f}{g}{n} draws a north-east dotted arrow
% with names f,g and length n units
\newcommand{\NNEDOTAR}[3]{\testdiagrammode%
\truex{100}\truey{268}\truez{134}%
\Z=#3%
\divide\Z by 2%
\NUMBEROFDOTS=#3%
\divide\NUMBEROFDOTS by \value{z}%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(0,0)%
\multiput(-\Z,-#3)(\value{z},\value{y}){\NUMBEROFDOTS}%
{\circle*{\value{x}}}%
\put(\Z,#3){\nnehead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \NNEMONO{f}{g}{n} draws a north-north-east monomorphism
% with names f,g and length n units
\newcommand{\NNEMONO}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\truetaiL%
\bimolength=#3%
\advance\bimolength by -\truemonotaiL%
\monolength=\bimolength%
\advance\monolength by -\Z%
\secondmonolength=\monolength%
\multiply\secondmonolength by 2%
\begin{picture}(0,0)%
\put(-\monolength,-\secondmonolength){\line(1,2){\bimolength}}%
\put(-\monolength,-\secondmonolength){\nnehead}%
\put(\Z,#3){\nnehead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \NNEEPI{f}{g}{n} draws a north-north-east epimorphism
% with names f, g and length n units
\newcommand{\NNEEPI}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\trueheaD%
\bimolength=#3%
\advance\bimolength by -\trueepiheaD%
\epilength=\bimolength%
\advance\epilength by -\Z%
\secondepilength=\epilength%
\multiply\secondepilength by 2%
\begin{picture}(0,0)%
\put(-\Z,-#3){\line(1,2){\bimolength}}%
\put(\epilength,\secondepilength){\nnehead}%
\put(\Z,#3){\nnehead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \NNEBIMO{f}{g}{n} draws a north-north-east bimorphism
% with names f,g and length n units
\newcommand{\NNEBIMO}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\truetaiL\trueheaD%
\bimolength=#3%
\advance\bimolength by -\truemonotaiL%
\monolength=\bimolength%
\advance\monolength by -\Z%
\advance\bimolength by -\trueepiheaD%
\epilength=\bimolength%
\advance\epilength by -\monolength%
\secondmonolength=\monolength%
\multiply\secondmonolength by 2%
\secondepilength=\epilength%
\multiply\secondepilength by 2%
\begin{picture}(0,0)%
\put(-\monolength,-\secondmonolength){\line(1,2){\bimolength}}%
\put(-\monolength,-\secondmonolength){\nnehead}%
\put(\epilength,\secondepilength){\nnehead}%
\put(\Z,#3){\nnehead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \NNEEQL{f}{g}{n} draws a north-north-east equality
% with names f,g and length n units
\newcommand{\NNEEQL}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(-\Z,-#3){\begin{picture}(0,0)%
\truex{44}\truey{89}%
\put(-\value{y},\value{x}){\line(1,2){#3}}%
\put(\value{y},-\value{x}){\line(1,2){#3}}%
\end{picture}}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \NNEBIAR{f}{g}{n} draws a pair of north-north-east arrows
% with names f,g and length n units
\newcommand{\NNEBIAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=#3%
\multiply \Z by 2%
\begin{picture}(0,0)%
\put(-\Y,-#3){\begin{picture}(0,0)%
\truex{313}\truey{156}%
\put(-\value{x},\value{y}){\line(1,2){#3}}%
\put(\value{x},-\value{y}){\line(1,2){#3}}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Z%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Z%
\advance\secondepilength by \value{y}%
\put(\monolength,\secondepilength){\nnehead}%
\put(\epilength,\secondmonolength){\nnehead}%
\end{picture}}
\truex{300}\truey{1000}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \NNEBIDIST{f}{g}{n} draws a pair of north-north-east distributors
% with names f,g and length n units
\newcommand{\NNEBIDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=#3%
\multiply \Z by 2%
\begin{picture}(0,0)%
\truex{313}\truey{156}\truez{400}%
\put(-\Y,-#3){\begin{picture}(0,0)%
\put(-\value{x},\value{y}){\line(1,2){#3}}%
\put(\value{x},-\value{y}){\line(1,2){#3}}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Z%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Z%
\advance\secondepilength by \value{y}%
\put(\monolength,\secondepilength){\nnehead}%
\put(\epilength,\secondmonolength){\nnehead}%
\end{picture}}
\put(-\value{x},\value{y}){\circle{\value{z}}}%
\put(\value{x},-\value{y}){\circle{\value{z}}}%
\truex{300}\truey{1000}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \NNEADJAR{f}{g}{n} draws a north-north-east pair of adjoint arrows
% with names f,g and length n units
\newcommand{\NNEADJAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=#3%
\multiply \Z by 2%
\begin{picture}(0,0)%
\put(-\Y,-#3){\begin{picture}(0,0)%
\truex{313}\truey{156}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Z%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Z%
\advance\secondepilength by \value{y}%
\put(\value{x},-\value{y}){\line(1,2){#3}}%
\put(\epilength,\secondmonolength){\nnehead}%
\put(\monolength,\secondepilength){\line(-1,-2){#3}}%
\put(-\value{x},\value{y}){\sswhead}%
\end{picture}}
\truex{300}\truey{1000}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \NNEADJDIST{f}{g}{n} draws a north-north-east pair of adjoint distributors
% with names f,g and length n units
\newcommand{\NNEADJDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=#3%
\multiply \Z by 2%
\begin{picture}(0,0)%
\truex{313}\truey{156}\truez{400}%
\put(-\Y,-#3){\begin{picture}(0,0)%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Z%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Z%
\advance\secondepilength by \value{y}%
\put(\value{x},-\value{y}){\line(1,2){#3}}%
\put(\epilength,\secondmonolength){\nnehead}%
\put(\monolength,\secondepilength){\line(-1,-2){#3}}%
\put(-\value{x},\value{y}){\sswhead}%
\end{picture}}
\put(-\value{x},\value{y}){\circle{\value{z}}}%
\put(\value{x},-\value{y}){\circle{\value{z}}}%
\truex{300}\truey{1000}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% The following commands produce north-north-east arrows;
% the default length is 6700 units
% basic north-north-east arrow
\def\basicnnear[#1]{\NNEAR{}{}{#100}}%
% north-north-east arrow
\newcommand{\nnear}{\@ifnextchar[{\basicnnear}{\basicnnear[67]}}%
% basic north-north-east arrow with upper name
\def\basicNnear[#1]#2{\NNEAR{#2}{}{#100}}%
% north-north-east arrow with upper name
\newcommand{\Nnear}{\@ifnextchar[{\basicNnear}{\basicNnear[67]}}%
% basic north-north-east arrow with lower name
\def\basicnneaR[#1]#2{\NNEAR{}{#2}{#100}}%
% north-north-east arrow with lower name
\newcommand{\nneaR}{\@ifnextchar[{\basicnneaR}{\basicnneaR[67]}}%
% basic north-north-east distributor
\def\basicnnedist[#1]{\NNEDIST{}{}{#100}}%
% north-north-east distributor
\newcommand{\nnedist}{\@ifnextchar[{\basicnnedist}{\basicnnedist[67]}}%
% basic north-north-east distributor with upper name
\def\basicNnedist[#1]#2{\NNEDIST{#2}{}{#100}}%
% north-north-east distributor with upper name
\newcommand{\Nnedist}{\@ifnextchar[{\basicNnedist}{\basicNnedist[67]}}%
% basic north-north-east distributor with lower name
\def\basicnnedisT[#1]#2{\NNEDIST{}{#2}{#100}}%
% north-north-east distributor with lower name
\newcommand{\nnedisT}{\@ifnextchar[{\basicnnedisT}{\basicnnedisT[67]}}%
% basic north-north-east dotted arrow
\def\basicnnedotar[#1]{\NNEDOTAR{}{}{#100}}%
% north-north-east dotted arrow
\newcommand{\nnedotar}{\@ifnextchar[{\basicnnedotar}{\basicnnedotar[67]}}%
% basic north-north-east dotted arrow with upper name
\def\basicNnedotar[#1]#2{\NNEDOTAR{#2}{}{#100}}%
% north-north-east dotted arrow with upper name
\newcommand{\Nnedotar}{\@ifnextchar[{\basicNnedotar}{\basicNnedotar[67]}}%
% basic north-north-east dotted arrow with lower name
\def\basicnnedotaR[#1]#2{\NNEDOTAR{}{#2}{#100}}%
% north-north-east dotted arrow with lower name
\newcommand{\nnedotaR}{\@ifnextchar[{\basicnnedotaR}{\basicnnedotaR[67]}}%
% basic north-north-east monomorphism
\def\basicnnemono[#1]{\NNEMONO{}{}{#100}}%
% north-north-east monomorphism
\newcommand{\nnemono}{\@ifnextchar[{\basicnnemono}{\basicnnemono[67]}}%
% basic north-north-east monomorphism with upper name
\def\basicNnemono[#1]#2{\NNEMONO{#2}{}{#100}}%
% north-north-east monomorphism with upper name
\newcommand{\Nnemono}{\@ifnextchar[{\basicNnemono}{\basicNnemono[67]}}%
% basic north-north-east monomorphism with lower name
\def\basicnnemonO[#1]#2{\NNEMONO{}{#2}{#100}}%
% north-north-east monomorphism with lower name
\newcommand{\nnemonO}{\@ifnextchar[{\basicnnemonO}{\basicnnemonO[67]}}%
% basic north-north-east epimorphism
\def\basicnneepi[#1]{\NNEEPI{}{}{#100}}%
% north-north-east epimorphism
\newcommand{\nneepi}{\@ifnextchar[{\basicnneepi}{\basicnneepi[67]}}%
% basic north-north-east epimorphism with upper name
\def\basicNneepi[#1]#2{\NNEEPI{#2}{}{#100}}%
% north-north-east epimorphism with upper name
\newcommand{\Nneepi}{\@ifnextchar[{\basicNneepi}{\basicNneepi[67]}}%
% basic north-north-east epimorphism with lower name
\def\basicnneepI[#1]#2{\NNEEPI{}{#2}{#100}}%
% north-north-east epimorphism with lower name
\newcommand{\nneepI}{\@ifnextchar[{\basicnneepI}{\basicnneepI[67]}}%
% basic north-north-east bimorphism
\def\basicnnebimo[#1]{\NNEBIMO{}{}{#100}}%
% north-north-east bimorphism
\newcommand{\nnebimo}{\@ifnextchar[{\basicnnebimo}{\basicnnebimo[67]}}%
% basic north-north-east bimorphism with upper name
\def\basicNnebimo[#1]#2{\NNEBIMO{#2}{}{#100}}%
% north-north-east bimorphism with upper name
\newcommand{\Nnebimo}{\@ifnextchar[{\basicNnebimo}{\basicNnebimo[67]}}%
% basic north-north-east bimorphism with lower name
\def\basicnnebimO[#1]#2{\NNEBIMO{}{#2}{#100}}%
% north-north-east bimorphism with lower name
\newcommand{\nnebimO}{\@ifnextchar[{\basicnnebimO}{\basicnnebimO[67]}}%
% basic north-north-east isomorphism
\def\basicnneiso[#1]{\NNEAR{\cong}{}{#100}}%
% north-north-east isomorphism
\newcommand{\nneiso}{\@ifnextchar[{\basicnneiso}{\basicnneiso[67]}}%
% basic north-north-east isomorphism with upper name
\def\basicNneiso[#1]#2{\NNEAR{#2}{\cong}{#100}}%
% north-north-east isomorphism with upper name
\newcommand{\Nneiso}{\@ifnextchar[{\basicNneiso}{\basicNneiso[67]}}%
% basic north-north-east isomorphism with lower name
\def\basicnneisO[#1]#2{\NNEAR{\cong}{#2}{#100}}%
% north-north-east isomorphism with lower name
\newcommand{\nneisO}{\@ifnextchar[{\basicnneisO}{\basicnneisO[67]}}%
% basic north-north-east equality
\def\basicnneeql[#1]{\NNEEQL{}{}{#100}}%
% north-north-east equality
\newcommand{\nneeql}{\@ifnextchar[{\basicnneeql}{\basicnneeql[67]}}%
% basic north-north-east equality with upper name
\def\basicNneeql[#1]#2{\NNEEQL{#2}{}{#100}}%
% north-north-east equality with upper name
\newcommand{\Nneeql}{\@ifnextchar[{\basicNneeql}{\basicNneeql[67]}}%
% basic north-north-east equality with lower name
\def\basicnneeqL[#1]#2{\NNEEQL{}{#2}{#100}}%
% north-north-east equality with lower name
\newcommand{\nneeqL}{\@ifnextchar[{\basicnneeqL}{\basicnneeqL[67]}}%
% basic north-north-east pair of arrows
\def\basicnnebiar[#1]{\NNEBIAR{}{}{#100}}%
% north-north-east pair of arrows
\newcommand{\nnebiar}{\@ifnextchar[{\basicnnebiar}{\basicnnebiar[67]}}%
% basic north-north-east pair of arrows with names
\def\basicNnebiar[#1]#2#3{\NNEBIAR{#2}{#3}{#100}}%
% north-north-east pair of arrows with names
\newcommand{\Nnebiar}{\@ifnextchar[{\basicNnebiar}{\basicNnebiar[67]}}%
\let\nnebiaR=\Nnebiar
% basic north-north-east pair of distributors
\def\basicnnebidist[#1]{\NNEBIDIST{}{}{#100}}%
% north-north-east pair of distributors
\newcommand{\nnebidist}{\@ifnextchar[{\basicnnebidist}{\basicnnebidist[67]}}%
% basic north-north-east pair of distributors with names
\def\basicNnebidist[#1]#2#3{\NNEBIDIST{#2}{#3}{#100}}%
% north-north-east pair of distributors with names
\newcommand{\Nnebidist}{\@ifnextchar[{\basicNnebidist}{\basicNnebidist[67]}}%
\let\nnebidisT=\Nnebidist
% basic north-north-east pair of adjoint arrows
\def\basicnneadjar[#1]{\NNEADJAR{}{}{#100}}%
% north-north-east pair of adjoint arrows
\newcommand{\nneadjar}{\@ifnextchar[{\basicnneadjar}{\basicnneadjar[67]}}%
% basic north-north-east pair of adjoint arrows with names
\def\basicNneadjar[#1]#2#3{\NNEADJAR{#2}{#3}{#100}}%
% north-north-east pair of adjoint arrows with names
\newcommand{\Nneadjar}{\@ifnextchar[{\basicNneadjar}{\basicNneadjar[67]}}%
\let\nneadjaR=\Nneadjar
% basic north-north-east pair of adjoint distributors
\def\basicnneadjdist[#1]{\NNEADJDIST{}{}{#100}}%
% north-north-east pair of adjoint distributors
\newcommand{\nneadjdist}{\@ifnextchar[{\basicnneadjdist}{\basicnneadjdist[67]}}%
% basic north-north-east pair of adjoint distributors with names
\def\basicNneadjdist[#1]#2#3{\NNEADJDIST{#2}{#3}{#100}}%
% north-north-east pair of adjoint distributors with names
\newcommand{\Nneadjdist}{\@ifnextchar[{\basicNneadjdist}{\basicNneadjdist[67]}}%
\let\nneadjdisT=\Nneadjdist
% SOUTH-SOUTH-EAST ARROWS
% The following commands produce south-south-east arrows
% of horizontal extent n units
% \SSEAR{f}{g}{n} draws a south-south-east arrow with names f, g
% and length n units
\newcommand{\SSEAR}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(-\Z,#3){\line(1,-2){#3}}%
\put(\Z,-#3){\ssehead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \SSEDIST{f}{g}{n} draws a south-south-east distributor
% with names f, g and length n units
\newcommand{\SSEDIST}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(-\Z,#3){\line(1,-2){#3}}%
\put(\Z,-#3){\ssehead}%
\truex{400}%
\put(0,0){\circle{\value{x}}}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \SSEDOTAR{f}{g}{n} draws a north-east dotted arrow
% with names f,g and length n units
\newcommand{\SSEDOTAR}[3]{\testdiagrammode%
\truex{100}\truey{268}\truez{134}%
\Z=#3%
\divide\Z by 2%
\NUMBEROFDOTS=#3%
\divide\NUMBEROFDOTS by \value{z}%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(0,0)%
\multiput(-\Z,#3)(\value{z},-\value{y}){\NUMBEROFDOTS}%
{\circle*{\value{x}}}%
\put(\Z,-#3){\ssehead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \SSEMONO{f}{g}{n} draws a south-south-east monomorphism
% with names f,g and length n units
\newcommand{\SSEMONO}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\truetaiL%
\bimolength=#3%
\advance\bimolength by -\truemonotaiL%
\monolength=\bimolength%
\advance\monolength by -\Z%
\secondmonolength=\monolength%
\multiply\secondmonolength by 2%
\begin{picture}(0,0)%
\put(-\monolength,\secondmonolength){\line(1,-2){\bimolength}}%
\put(-\monolength,\secondmonolength){\ssehead}%
\put(\Z,-#3){\ssehead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \SSEEPI{f}{g}{n} draws a south-south-east epimorphism
% with names f, g and length n units
\newcommand{\SSEEPI}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\trueheaD%
\bimolength=#3%
\advance\bimolength by -\trueepiheaD%
\epilength=\bimolength%
\advance\epilength by -\Z%
\secondepilength=\epilength%
\multiply\secondepilength by 2%
\begin{picture}(0,0)%
\put(-\Z,#3){\line(1,-2){\bimolength}}%
\put(\epilength,-\secondepilength){\ssehead}%
\put(\Z,-#3){\ssehead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \SSEBIMO{f}{g}{n} draws a south-south-east bimorphism
% with names f,g and length n units
\newcommand{\SSEBIMO}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\truetaiL\trueheaD%
\bimolength=#3%
\advance\bimolength by -\truemonotaiL%
\monolength=\bimolength%
\advance\monolength by -\Z%
\advance\bimolength by -\trueepiheaD%
\epilength=\bimolength%
\advance\epilength by -\monolength%
\secondmonolength=\monolength%
\multiply\secondmonolength by 2%
\secondepilength=\epilength%
\multiply\secondepilength by 2%
\begin{picture}(0,0)%
\put(-\monolength,\secondmonolength){\line(1,-2){\bimolength}}%
\put(-\monolength,\secondmonolength){\ssehead}%
\put(\epilength,-\secondepilength){\ssehead}%
\put(\Z,-#3){\ssehead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \SSEEQL{f}{g}{n} draws a south-south-east equality
% with names f,g and length n units
\newcommand{\SSEEQL}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(-\Z,#3){\begin{picture}(0,0)%
\truex{44}\truey{89}%
\put(-\value{y},-\value{x}){\line(1,-2){#3}}%
\put(\value{y},\value{x}){\line(1,-2){#3}}%
\end{picture}}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \SSEBIAR{f}{g}{n} draws a pair of south-south-east arrows
% with names f,g and length n units
\newcommand{\SSEBIAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=#3%
\multiply \Z by 2%
\begin{picture}(0,0)%
\put(-\Y,#3){\begin{picture}(0,0)%
\truex{313}\truey{156}%
\put(-\value{x},-\value{y}){\line(1,-2){#3}}%
\put(\value{x},\value{y}){\line(1,-2){#3}}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Z%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Z%
\advance\secondepilength by \value{y}%
\put(\monolength,-\secondepilength){\ssehead}%
\put(\epilength,-\secondmonolength){\ssehead}%
\end{picture}}
\truex{400}\truey{1000}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \SSEBIDIST{f}{g}{n} draws a pair of south-south-east distributors
% with names f,g and length n units
\newcommand{\SSEBIDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=#3%
\multiply \Z by 2%
\begin{picture}(0,0)%
\truex{313}\truey{156}\truez{400}%
\put(-\Y,#3){\begin{picture}(0,0)%
\put(-\value{x},-\value{y}){\line(1,-2){#3}}%
\put(\value{x},\value{y}){\line(1,-2){#3}}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Z%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Z%
\advance\secondepilength by \value{y}%
\put(\monolength,-\secondepilength){\ssehead}%
\put(\epilength,-\secondmonolength){\ssehead}%
\end{picture}}
\put(-\value{x},-\value{y}){\circle{\value{z}}}%
\put(\value{x},\value{y}){\circle{\value{z}}}%
\truex{500}\truey{1000}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \SSEADJAR{f}{g}{n} draws a south-south-east pair of adjoint arrows
% with names f,g and length n units
\newcommand{\SSEADJAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=#3%
\multiply \Z by 2%
\begin{picture}(0,0)%
\put(-\Y,#3){\begin{picture}(0,0)%
\truex{313}\truey{156}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Z%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Z%
\advance\secondepilength by \value{y}%
\put(-\value{x},-\value{y}){\line(1,-2){#3}}%
\put(\monolength,-\secondepilength){\ssehead}%
\put(\epilength,-\secondmonolength){\line(-1,2){#3}}%
\put(\value{x},\value{y}){\nnwhead}%
\end{picture}}
\truex{400}\truey{1000}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \SSEADJDIST{f}{g}{n} draws a south-south-east pair of adjoint distributors
% with names f,g and length n units
\newcommand{\SSEADJDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=#3%
\multiply \Z by 2%
\begin{picture}(0,0)%
\truex{313}\truey{156}\truez{400}%
\put(-\Y,#3){\begin{picture}(0,0)%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Z%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Z%
\advance\secondepilength by \value{y}%
\put(-\value{x},-\value{y}){\line(1,-2){#3}}%
\put(\monolength,-\secondepilength){\ssehead}%
\put(\epilength,-\secondmonolength){\line(-1,2){#3}}%
\put(\value{x},\value{y}){\nnwhead}%
\end{picture}}
\put(\value{x},\value{y}){\circle{\value{z}}}%
\put(-\value{x},-\value{y}){\circle{\value{z}}}%
\truex{500}\truey{1000}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% The following commands produce south-south-east arrows;
% the default length is 6700 units
% basic south-south-east arrow
\def\basicssear[#1]{\SSEAR{}{}{#100}}%
% south-south-east arrow
\newcommand{\ssear}{\@ifnextchar[{\basicssear}{\basicssear[67]}}%
% basic south-south-east arrow with upper name
\def\basicSsear[#1]#2{\SSEAR{#2}{}{#100}}%
% south-south-east arrow with upper name
\newcommand{\Ssear}{\@ifnextchar[{\basicSsear}{\basicSsear[67]}}%
% basic south-south-east arrow with lower name
\def\basicsseaR[#1]#2{\SSEAR{}{#2}{#100}}%
% south-south-east arrow with lower name
\newcommand{\sseaR}{\@ifnextchar[{\basicsseaR}{\basicsseaR[67]}}%
% basic south-south-east distributor
\def\basicssedist[#1]{\SSEDIST{}{}{#100}}%
% south-south-east distributor
\newcommand{\ssedist}{\@ifnextchar[{\basicssedist}{\basicssedist[67]}}%
% basic south-south-east distributor with upper name
\def\basicSsedist[#1]#2{\SSEDIST{#2}{}{#100}}%
% south-south-east distributor with upper name
\newcommand{\Ssedist}{\@ifnextchar[{\basicSsedist}{\basicSsedist[67]}}%
% basic south-south-east distributor with lower name
\def\basicssedisT[#1]#2{\SSEDIST{}{#2}{#100}}%
% south-south-east distributor with lower name
\newcommand{\ssedisT}{\@ifnextchar[{\basicssedisT}{\basicssedisT[67]}}%
% basic south-south-east dotted arrow
\def\basicssedotar[#1]{\SSEDOTAR{}{}{#100}}%
% south-south-east dotted arrow
\newcommand{\ssedotar}{\@ifnextchar[{\basicssedotar}{\basicssedotar[67]}}%
% basic south-south-east dotted arrow with upper name
\def\basicSsedotar[#1]#2{\SSEDOTAR{#2}{}{#100}}%
% south-south-east dotted arrow with upper name
\newcommand{\Ssedotar}{\@ifnextchar[{\basicSsedotar}{\basicSsedotar[67]}}%
% basic south-south-east dotted arrow with lower name
\def\basicssedotaR[#1]#2{\SSEDOTAR{}{#2}{#100}}%
% south-south-east dotted arrow with lower name
\newcommand{\ssedotaR}{\@ifnextchar[{\basicssedotaR}{\basicssedotaR[67]}}%
% basic south-south-east monomorphism
\def\basicssemono[#1]{\SSEMONO{}{}{#100}}%
% south-south-east monomorphism
\newcommand{\ssemono}{\@ifnextchar[{\basicssemono}{\basicssemono[67]}}%
% basic south-south-east monomorphism with upper name
\def\basicSsemono[#1]#2{\SSEMONO{#2}{}{#100}}%
% south-south-east monomorphism with upper name
\newcommand{\Ssemono}{\@ifnextchar[{\basicSsemono}{\basicSsemono[67]}}%
% basic south-south-east monomorphism with lower name
\def\basicssemonO[#1]#2{\SSEMONO{}{#2}{#100}}%
% south-south-east monomorphism with lower name
\newcommand{\ssemonO}{\@ifnextchar[{\basicssemonO}{\basicssemonO[67]}}%
% basic south-south-east epimorphism
\def\basicsseepi[#1]{\SSEEPI{}{}{#100}}%
% south-south-east epimorphism
\newcommand{\sseepi}{\@ifnextchar[{\basicsseepi}{\basicsseepi[67]}}%
% basic south-south-east epimorphism with upper name
\def\basicSseepi[#1]#2{\SSEEPI{#2}{}{#100}}%
% south-south-east epimorphism with upper name
\newcommand{\Sseepi}{\@ifnextchar[{\basicSseepi}{\basicSseepi[67]}}%
% basic south-south-east epimorphism with lower name
\def\basicsseepI[#1]#2{\SSEEPI{}{#2}{#100}}%
% south-south-east epimorphism with lower name
\newcommand{\sseepI}{\@ifnextchar[{\basicsseepI}{\basicsseepI[67]}}%
% basic south-south-east bimorphism
\def\basicssebimo[#1]{\SSEBIMO{}{}{#100}}%
% south-south-east bimorphism
\newcommand{\ssebimo}{\@ifnextchar[{\basicssebimo}{\basicssebimo[67]}}%
% basic south-south-east bimorphism with upper name
\def\basicSsebimo[#1]#2{\SSEBIMO{#2}{}{#100}}%
% south-south-east bimorphism with upper name
\newcommand{\Ssebimo}{\@ifnextchar[{\basicSsebimo}{\basicSsebimo[67]}}%
% basic south-south-east bimorphism with lower name
\def\basicssebimO[#1]#2{\SSEBIMO{}{#2}{#100}}%
% south-south-east bimorphism with lower name
\newcommand{\ssebimO}{\@ifnextchar[{\basicssebimO}{\basicssebimO[67]}}%
% basic south-south-east isomorphism
\def\basicsseiso[#1]{\SSEAR{\cong}{}{#100}}%
% south-south-east isomorphism
\newcommand{\sseiso}{\@ifnextchar[{\basicsseiso}{\basicsseiso[67]}}%
% basic south-south-east isomorphism with upper name
\def\basicSseiso[#1]#2{\SSEAR{#2}{\cong}{#100}}%
% south-south-east isomorphism with upper name
\newcommand{\Sseiso}{\@ifnextchar[{\basicSseiso}{\basicSseiso[67]}}%
% basic south-south-east isomorphism with lower name
\def\basicsseisO[#1]#2{\SSEAR{\cong}{#2}{#100}}%
% south-south-east isomorphism with lower name
\newcommand{\sseisO}{\@ifnextchar[{\basicsseisO}{\basicsseisO[67]}}%
% basic south-south-east equality
\def\basicsseeql[#1]{\SSEEQL{}{}{#100}}%
% south-south-east equality
\newcommand{\sseeql}{\@ifnextchar[{\basicsseeql}{\basicsseeql[67]}}%
% basic south-south-east equality with upper name
\def\basicSseeql[#1]#2{\SSEEQL{#2}{}{#100}}%
% south-south-east equality with upper name
\newcommand{\Sseeql}{\@ifnextchar[{\basicSseeql}{\basicSseeql[67]}}%
% basic south-south-east equality with lower name
\def\basicsseeqL[#1]#2{\SSEEQL{}{#2}{#100}}%
% south-south-east equality with lower name
\newcommand{\sseeqL}{\@ifnextchar[{\basicsseeqL}{\basicsseeqL[67]}}%
% basic south-south-east pair of arrows
\def\basicssebiar[#1]{\SSEBIAR{}{}{#100}}%
% south-south-east pair of arrows
\newcommand{\ssebiar}{\@ifnextchar[{\basicssebiar}{\basicssebiar[67]}}%
% basic south-south-east pair of arrows with names
\def\basicSsebiar[#1]#2#3{\SSEBIAR{#2}{#3}{#100}}%
% south-south-east pair of arrows with names
\newcommand{\Ssebiar}{\@ifnextchar[{\basicSsebiar}{\basicSsebiar[67]}}%
\let\ssebiaR=\Ssebiar
% basic south-south-east pair of distributors
\def\basicssebidist[#1]{\SSEBIDIST{}{}{#100}}%
% south-south-east pair of distributors
\newcommand{\ssebidist}{\@ifnextchar[{\basicssebidist}{\basicssebidist[67]}}%
% basic south-south-east pair of distributors with names
\def\basicSsebidist[#1]#2#3{\SSEBIDIST{#2}{#3}{#100}}%
% south-south-east pair of distributors with names
\newcommand{\Ssebidist}{\@ifnextchar[{\basicSsebidist}{\basicSsebidist[67]}}%
\let\ssebidisT=\Ssebidist
% basic south-south-east pair of adjoint arrows
\def\basicsseadjar[#1]{\SSEADJAR{}{}{#100}}%
% south-south-east pair of adjoint arrows
\newcommand{\sseadjar}{\@ifnextchar[{\basicsseadjar}{\basicsseadjar[67]}}%
% basic south-south-east pair of adjoint arrows with names
\def\basicSseadjar[#1]#2#3{\SSEADJAR{#2}{#3}{#100}}%
% south-south-east pair of adjoint arrows with names
\newcommand{\Sseadjar}{\@ifnextchar[{\basicSseadjar}{\basicSseadjar[67]}}%
\let\sseadjaR=\Sseadjar
% basic south-south-east pair of adjoint distributors
\def\basicsseadjdist[#1]{\SSEADJDIST{}{}{#100}}%
% south-south-east pair of adjoint distributors
\newcommand{\sseadjdist}{\@ifnextchar[{\basicsseadjdist}{\basicsseadjdist[67]}}%
% basic south-south-east pair of adjoint distributors with names
\def\basicSseadjdist[#1]#2#3{\SSEADJDIST{#2}{#3}{#100}}%
% south-south-east pair of adjoint distributors with names
\newcommand{\Sseadjdist}{\@ifnextchar[{\basicSseadjdist}{\basicSseadjdist[67]}}%
\let\sseadjdisT=\Sseadjdist
% SOUTH-SOUTH-WEST ARROWS
% The following commands produce south-south-west arrows
% of horizontal extent n units
% \SSWAR{f}{g}{n} draws a south-south-west arrow with names f, g
% and length n units
\newcommand{\SSWAR}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(\Z,#3){\line(-1,-2){#3}}%
\put(-\Z,-#3){\sswhead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \SSWDIST{f}{g}{n} draws a south-south-west distributor
% with names f, g and length n units
\newcommand{\SSWDIST}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(\Z,#3){\line(-1,-2){#3}}%
\put(-\Z,-#3){\sswhead}%
\truex{400}%
\put(0,0){\circle{\value{x}}}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \SSWDOTAR{f}{g}{n} draws a north-east dotted arrow
% with names f,g and length n units
\newcommand{\SSWDOTAR}[3]{\testdiagrammode%
\truex{100}\truey{268}\truez{134}%
\Z=#3%
\divide\Z by 2%
\NUMBEROFDOTS=#3%
\divide\NUMBEROFDOTS by \value{z}%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(0,0)%
\multiput(\Z,#3)(-\value{z},-\value{y}){\NUMBEROFDOTS}%
{\circle*{\value{x}}}%
\put(-\Z,-#3){\sswhead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \SSWMONO{f}{g}{n} draws a south-south-west monomorphism
% with names f,g and length n units
\newcommand{\SSWMONO}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\truetaiL%
\bimolength=#3%
\advance\bimolength by -\truemonotaiL%
\monolength=\bimolength%
\advance\monolength by -\Z%
\secondmonolength=\monolength%
\multiply\secondmonolength by 2%
\begin{picture}(0,0)%
\put(\monolength,\secondmonolength){\line(-1,-2){\bimolength}}%
\put(\monolength,\secondmonolength){\sswhead}%
\put(-\Z,-#3){\sswhead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \SSWEPI{f}{g}{n} draws a south-south-west epimorphism
% with names f, g and length n units
\newcommand{\SSWEPI}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\trueheaD%
\bimolength=#3%
\advance\bimolength by -\trueepiheaD%
\epilength=\bimolength%
\advance\epilength by -\Z%
\secondepilength=\epilength%
\multiply\secondepilength by 2%
\begin{picture}(0,0)%
\put(\Z,#3){\line(-1,-2){\bimolength}}%
\put(-\epilength,-\secondepilength){\sswhead}%
\put(-\Z,-#3){\sswhead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \SSWBIMO{f}{g}{n} draws a south-south-west bimorphism
% with names f,g and length n units
\newcommand{\SSWBIMO}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\truetaiL\trueheaD%
\bimolength=#3%
\advance\bimolength by -\truemonotaiL%
\monolength=\bimolength%
\advance\monolength by -\Z%
\advance\bimolength by -\trueepiheaD%
\epilength=\bimolength%
\advance\epilength by -\monolength%
\secondmonolength=\monolength%
\multiply\secondmonolength by 2%
\secondepilength=\epilength%
\multiply\secondepilength by 2%
\begin{picture}(0,0)%
\put(\monolength,\secondmonolength){\line(-1,-2){\bimolength}}%
\put(\monolength,\secondmonolength){\sswhead}%
\put(-\epilength,-\secondepilength){\sswhead}%
\put(-\Z,-#3){\sswhead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \SSWBIAR{f}{g}{n} draws a pair of south-south-west arrows
% with names f,g and length n units
\newcommand{\SSWBIAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=#3%
\multiply \Z by 2%
\begin{picture}(0,0)%
\put(\Y,#3){\begin{picture}(0,0)%
\truex{313}\truey{156}%
\put(-\value{x},\value{y}){\line(-1,-2){#3}}%
\put(\value{x},-\value{y}){\line(-1,-2){#3}}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Z%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Z%
\advance\secondepilength by \value{y}%
\put(-\monolength,-\secondepilength){\sswhead}%
\put(-\epilength,-\secondmonolength){\sswhead}%
\end{picture}}
\truex{300}\truey{1000}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \SSWBIDIST{f}{g}{n} draws a pair of south-south-west distributors
% with names f,g and length n units
\newcommand{\SSWBIDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=#3%
\multiply \Z by 2%
\begin{picture}(0,0)%
\truex{313}\truey{156}\truez{400}%
\put(\Y,#3){\begin{picture}(0,0)%
\put(-\value{x},\value{y}){\line(-1,-2){#3}}%
\put(\value{x},-\value{y}){\line(-1,-2){#3}}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Z%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Z%
\advance\secondepilength by \value{y}%
\put(-\monolength,-\secondepilength){\sswhead}%
\put(-\epilength,-\secondmonolength){\sswhead}%
\end{picture}}
\put(-\value{x},\value{y}){\circle{\value{z}}}%
\put(\value{x},-\value{y}){\circle{\value{z}}}%
\truex{300}\truey{1000}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \SSWADJAR{f}{g}{n} draws a south-south-west pair of adjoint arrows
% with names f,g and length n units
\newcommand{\SSWADJAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=#3%
\multiply \Z by 2%
\begin{picture}(0,0)%
\put(\Y,#3){\begin{picture}(0,0)%
\truex{313}\truey{156}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Z%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Z%
\advance\secondepilength by \value{y}%
\put(\value{x},-\value{y}){\line(-1,-2){#3}}%
\put(-\monolength,-\secondepilength){\sswhead}%
\put(-\epilength,-\secondmonolength){\line(1,2){#3}}%
\put(-\value{x},\value{y}){\nnehead}%
\end{picture}}
\truex{300}\truey{1000}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% \SSWADJDIST{f}{g}{n} draws a south-south-west pair of adjoint distributors
% with names f,g and length n units
\newcommand{\SSWADJDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=#3%
\multiply \Z by 2%
\begin{picture}(0,0)%
\truex{313}\truey{156}\truez{400}%
\put(\Y,#3){\begin{picture}(0,0)%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Z%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Z%
\advance\secondepilength by \value{y}%
\put(\value{x},-\value{y}){\line(-1,-2){#3}}%
\put(-\monolength,-\secondepilength){\sswhead}%
\put(-\epilength,-\secondmonolength){\line(1,2){#3}}%
\put(-\value{x},\value{y}){\nnehead}%
\end{picture}}
\put(-\value{x},\value{y}){\circle{\value{z}}}%
\put(\value{x},-\value{y}){\circle{\value{z}}}%
\truex{300}\truey{1000}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% The following commands produce south-south-west arrows;
% the default length is 6700 units
% basic south-south-west arrow
\def\basicsswar[#1]{\SSWAR{}{}{#100}}%
% south-south-west arrow
\newcommand{\sswar}{\@ifnextchar[{\basicsswar}{\basicsswar[67]}}%
% basic south-south-west arrow with upper name
\def\basicSswar[#1]#2{\SSWAR{#2}{}{#100}}%
% south-south-west arrow with upper name
\newcommand{\Sswar}{\@ifnextchar[{\basicSswar}{\basicSswar[67]}}%
% basic south-south-west arrow with lower name
\def\basicsswaR[#1]#2{\SSWAR{}{#2}{#100}}%
% south-south-west arrow with lower name
\newcommand{\sswaR}{\@ifnextchar[{\basicsswaR}{\basicsswaR[67]}}%
% basic south-south-west distributor
\def\basicsswdist[#1]{\SSWDIST{}{}{#100}}%
% south-south-west distributor
\newcommand{\sswdist}{\@ifnextchar[{\basicsswdist}{\basicsswdist[67]}}%
% basic south-south-west distributor with upper name
\def\basicSswdist[#1]#2{\SSWDIST{#2}{}{#100}}%
% south-south-west distributor with upper name
\newcommand{\Sswdist}{\@ifnextchar[{\basicSswdist}{\basicSswdist[67]}}%
% basic south-south-west distributor with lower name
\def\basicsswdisT[#1]#2{\SSWDIST{}{#2}{#100}}%
% south-south-west distributor with lower name
\newcommand{\sswdisT}{\@ifnextchar[{\basicsswdisT}{\basicsswdisT[67]}}%
% basic south-south-west dotted arrow
\def\basicsswdotar[#1]{\SSWDOTAR{}{}{#100}}%
% south-south-west dotted arrow
\newcommand{\sswdotar}{\@ifnextchar[{\basicsswdotar}{\basicsswdotar[67]}}%
% basic south-south-west dotted arrow with upper name
\def\basicSswdotar[#1]#2{\SSWDOTAR{#2}{}{#100}}%
% south-south-west dotted arrow with upper name
\newcommand{\Sswdotar}{\@ifnextchar[{\basicSswdotar}{\basicSswdotar[67]}}%
% basic south-south-west dotted arrow with lower name
\def\basicsswdotaR[#1]#2{\SSWDOTAR{}{#2}{#100}}%
% south-south-west dotted arrow with lower name
\newcommand{\sswdotaR}{\@ifnextchar[{\basicsswdotaR}{\basicsswdotaR[67]}}%
% basic south-south-west monomorphism
\def\basicsswmono[#1]{\SSWMONO{}{}{#100}}%
% south-south-west monomorphism
\newcommand{\sswmono}{\@ifnextchar[{\basicsswmono}{\basicsswmono[67]}}%
% basic south-south-west monomorphism with upper name
\def\basicSswmono[#1]#2{\SSWMONO{#2}{}{#100}}%
% south-south-west monomorphism with upper name
\newcommand{\Sswmono}{\@ifnextchar[{\basicSswmono}{\basicSswmono[67]}}%
% basic south-south-west monomorphism with lower name
\def\basicsswmonO[#1]#2{\SSWMONO{}{#2}{#100}}%
% south-south-west monomorphism with lower name
\newcommand{\sswmonO}{\@ifnextchar[{\basicsswmonO}{\basicsswmonO[67]}}%
% basic south-south-west epimorphism
\def\basicsswepi[#1]{\SSWEPI{}{}{#100}}%
% south-south-west epimorphism
\newcommand{\sswepi}{\@ifnextchar[{\basicsswepi}{\basicsswepi[67]}}%
% basic south-south-west epimorphism with upper name
\def\basicSswepi[#1]#2{\SSWEPI{#2}{}{#100}}%
% south-south-west epimorphism with upper name
\newcommand{\Sswepi}{\@ifnextchar[{\basicSswepi}{\basicSswepi[67]}}%
% basic south-south-west epimorphism with lower name
\def\basicsswepI[#1]#2{\SSWEPI{}{#2}{#100}}%
% south-south-west epimorphism with lower name
\newcommand{\sswepI}{\@ifnextchar[{\basicsswepI}{\basicsswepI[67]}}%
% basic south-south-west bimorphism
\def\basicsswbimo[#1]{\SSWBIMO{}{}{#100}}%
% south-south-west bimorphism
\newcommand{\sswbimo}{\@ifnextchar[{\basicsswbimo}{\basicsswbimo[67]}}%
% basic south-south-west bimorphism with upper name
\def\basicSswbimo[#1]#2{\SSWBIMO{#2}{}{#100}}%
% south-south-west bimorphism with upper name
\newcommand{\Sswbimo}{\@ifnextchar[{\basicSswbimo}{\basicSswbimo[67]}}%
% basic south-south-west bimorphism with lower name
\def\basicsswbimO[#1]#2{\SSWBIMO{}{#2}{#100}}%
% south-south-west bimorphism with lower name
\newcommand{\sswbimO}{\@ifnextchar[{\basicsswbimO}{\basicsswbimO[67]}}%
% basic south-south-west isomorphism
\def\basicsswiso[#1]{\SSWAR{\cong}{}{#100}}%
% south-south-west isomorphism
\newcommand{\sswiso}{\@ifnextchar[{\basicsswiso}{\basicsswiso[67]}}%
% basic south-south-west isomorphism with upper name
\def\basicSswiso[#1]#2{\SSWAR{#2}{\cong}{#100}}%
% south-south-west isomorphism with upper name
\newcommand{\Sswiso}{\@ifnextchar[{\basicSswiso}{\basicSswiso[67]}}%
% basic south-south-west isomorphism with lower name
\def\basicsswisO[#1]#2{\SSWAR{\cong}{#2}{#100}}%
% south-south-west isomorphism with lower name
\newcommand{\sswisO}{\@ifnextchar[{\basicsswisO}{\basicsswisO[67]}}%
% south-south-west equality
\let\ssweql=\nneeql%
% south-south-west equality with upper name
\let\Ssweql=\Nneeql%
% south-south-west equality with lower name
\let\ssweqL=\nneeqL%
% basic south-south-west pair of arrows
\def\basicsswbiar[#1]{\SSWBIAR{}{}{#100}}%
% south-south-west pair of arrows
\newcommand{\sswbiar}{\@ifnextchar[{\basicsswbiar}{\basicsswbiar[67]}}%
% basic south-south-west pair of arrows with names
\def\basicSswbiar[#1]#2#3{\SSWBIAR{#2}{#3}{#100}}%
% south-south-west pair of arrows with names
\newcommand{\Sswbiar}{\@ifnextchar[{\basicSswbiar}{\basicSswbiar[67]}}%
\let\sswbiaR=\Sswbiar
% basic south-south-west pair of distributors
\def\basicsswbidist[#1]{\SSWBIDIST{}{}{#100}}%
% south-south-west pair of distributors
\newcommand{\sswbidist}{\@ifnextchar[{\basicsswbidist}{\basicsswbidist[67]}}%
% basic south-south-west pair of distributors with names
\def\basicSswbidist[#1]#2#3{\SSWBIDIST{#2}{#3}{#100}}%
% south-south-west pair of distributors with names
\newcommand{\Sswbidist}{\@ifnextchar[{\basicSswbidist}{\basicSswbidist[67]}}%
\let\sswbidisT=\Sswbidist
% basic south-south-west pair of adjoint arrows
\def\basicsswadjar[#1]{\SSWADJAR{}{}{#100}}%
% south-south-west pair of adjoint arrows
\newcommand{\sswadjar}{\@ifnextchar[{\basicsswadjar}{\basicsswadjar[67]}}%
% basic south-south-west pair of adjoint arrows with names
\def\basicSswadjar[#1]#2#3{\SSWADJAR{#2}{#3}{#100}}%
% south-south-west pair of adjoint arrows with names
\newcommand{\Sswadjar}{\@ifnextchar[{\basicSswadjar}{\basicSswadjar[67]}}%
\let\sswadjaR=\Sswadjar
% basic south-south-west pair of adjoint distributors
\def\basicsswadjdist[#1]{\SSWADJDIST{}{}{#100}}%
% south-south-west pair of adjoint distributors
\newcommand{\sswadjdist}{\@ifnextchar[{\basicsswadjdist}{\basicsswadjdist[67]}}%
% basic south-south-west pair of adjoint distributors with names
\def\basicSswadjdist[#1]#2#3{\SSWADJDIST{#2}{#3}{#100}}%
% south-south-west pair of adjoint distributors with names
\newcommand{\Sswadjdist}{\@ifnextchar[{\basicSswadjdist}{\basicSswadjdist[67]}}%
\let\sswadjdisT=\Sswadjdist
% NORTH-NORTH-WEST ARROWS
% The following commands produce north-north-west arrows
% of horizontal extent n units
% \NNWAR{f}{g}{n} draws a north-north-west arrow with names f, g
% and length n units
\newcommand{\NNWAR}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(\Z,-#3){\line(-1,2){#3}}%
\put(-\Z,#3){\nnwhead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \NNWDIST{f}{g}{n} draws a north-north-west distributor
% with names f, g and length n units
\newcommand{\NNWDIST}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\begin{picture}(0,0)%
\put(\Z,-#3){\line(-1,2){#3}}%
\put(-\Z,#3){\nnwhead}%
\truex{400}%
\put(0,0){\circle{\value{x}}}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \NNWDOTAR{f}{g}{n} draws a north-east dotted arrow
% with names f,g and length n units
\newcommand{\NNWDOTAR}[3]{\testdiagrammode%
\truex{100}\truey{268}\truez{134}%
\Z=#3%
\divide\Z by 2%
\NUMBEROFDOTS=#3%
\divide\NUMBEROFDOTS by \value{z}%
\advance\NUMBEROFDOTS by 1%
\begin{picture}(0,0)%
\multiput(\Z,-#3)(-\value{z},\value{y}){\NUMBEROFDOTS}%
{\circle*{\value{x}}}%
\put(-\Z,#3){\nnwhead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \NNWMONO{f}{g}{n} draws a north-north-west monomorphism
% with names f,g and length n units
\newcommand{\NNWMONO}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\truetaiL%
\bimolength=#3%
\advance\bimolength by -\truemonotaiL%
\monolength=\bimolength%
\advance\monolength by -\Z%
\secondmonolength=\monolength%
\multiply\secondmonolength by 2%
\begin{picture}(0,0)%
\put(\monolength,-\secondmonolength){\line(-1,2){\bimolength}}%
\put(\monolength,-\secondmonolength){\nnwhead}%
\put(-\Z,#3){\nnwhead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \NNWEPI{f}{g}{n} draws a north-north-west epimorphism
% with names f, g and length n units
\newcommand{\NNWEPI}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\trueheaD%
\bimolength=#3%
\advance\bimolength by -\trueepiheaD%
\epilength=\bimolength%
\advance\epilength by -\Z%
\secondepilength=\epilength%
\multiply\secondepilength by 2%
\begin{picture}(0,0)%
\put(\Z,-#3){\line(-1,2){\bimolength}}%
\put(-\epilength,\secondepilength){\nnwhead}%
\put(-\Z,#3){\nnwhead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \NNWBIMO{f}{g}{n} draws a north-north-west bimorphism
% with names f,g and length n units
\newcommand{\NNWBIMO}[3]{\testdiagrammode%
\Z=#3%
\divide\Z by 2%
\truetaiL\trueheaD%
\bimolength=#3%
\advance\bimolength by -\truemonotaiL%
\monolength=\bimolength%
\advance\monolength by -\Z%
\advance\bimolength by -\trueepiheaD%
\epilength=\bimolength%
\advance\epilength by -\monolength%
\secondmonolength=\monolength%
\multiply\secondmonolength by 2%
\secondepilength=\epilength%
\multiply\secondepilength by 2%
\begin{picture}(0,0)%
\put(\monolength,-\secondmonolength){\line(-1,2){\bimolength}}%
\put(\monolength,-\secondmonolength){\nnwhead}%
\put(-\epilength,\secondepilength){\nnwhead}%
\put(-\Z,#3){\nnwhead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \NNWBIAR{f}{g}{n} draws a pair of north-north-west arrows
% with names f,g and length n units
\newcommand{\NNWBIAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=#3%
\multiply \Z by 2%
\begin{picture}(0,0)%
\put(\Y,-#3){\begin{picture}(0,0)%
\truex{313}\truey{156}%
\put(-\value{x},-\value{y}){\line(-1,2){#3}}%
\put(\value{x},\value{y}){\line(-1,2){#3}}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Z%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Z%
\advance\secondepilength by \value{y}%
\put(-\monolength,\secondepilength){\nnwhead}%
\put(-\epilength,\secondmonolength){\nnwhead}%
\end{picture}}
\truex{400}\truey{1000}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \NNWBIDIST{f}{g}{n} draws a pair of north-north-west distributors
% with names f,g and length n units
\newcommand{\NNWBIDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=#3%
\multiply \Z by 2%
\begin{picture}(0,0)%
\truex{313}\truey{156}\truez{400}%
\put(\Y,-#3){\begin{picture}(0,0)%
\put(-\value{x},-\value{y}){\line(-1,2){#3}}%
\put(\value{x},\value{y}){\line(-1,2){#3}}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Z%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Z%
\advance\secondepilength by \value{y}%
\put(-\monolength,\secondepilength){\nnwhead}%
\put(-\epilength,\secondmonolength){\nnwhead}%
\end{picture}}
\put(-\value{x},-\value{y}){\circle{\value{z}}}%
\put(\value{x},\value{y}){\circle{\value{z}}}%
\truex{500}\truey{1000}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \NNWADJAR{f}{g}{n} draws a north-north-west pair of adjoint arrows
% with names f,g and length n units
\newcommand{\NNWADJAR}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=#3%
\multiply \Z by 2%
\begin{picture}(0,0)%
\put(\Y,-#3){\begin{picture}(0,0)%
\truex{313}\truey{156}%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Z%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Z%
\advance\secondepilength by \value{y}%
\put(-\value{x},-\value{y}){\line(-1,2){#3}}%
\put(-\epilength,\secondmonolength){\nnwhead}%
\put(-\monolength,\secondepilength){\line(1,-2){#3}}%
\put(\value{x},\value{y}){\ssehead}%
\end{picture}}
\truex{400}\truey{1000}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% \NNWADJDIST{f}{g}{n} draws a north-north-west pair of adjoint distributors
% with names f,g and length n units
\newcommand{\NNWADJDIST}[3]{\testdiagrammode%
\Y=#3%
\divide\Y by 2%
\Z=#3%
\multiply \Z by 2%
\begin{picture}(0,0)%
\truex{313}\truey{156}\truez{400}%
\put(\Y,-#3){\begin{picture}(0,0)%
\monolength=#3%
\advance\monolength by -\value{x}%
\epilength=#3%
\advance\epilength by \value{x}%
\secondmonolength=\Z%
\advance\secondmonolength by -\value{y}%
\secondepilength=\Z%
\advance\secondepilength by \value{y}%
\put(-\value{x},-\value{y}){\line(-1,2){#3}}%
\put(-\epilength,\secondmonolength){\nnwhead}%
\put(-\monolength,\secondepilength){\line(1,-2){#3}}%
\put(\value{x},\value{y}){\ssehead}%
\end{picture}}
\put(\value{x},\value{y}){\circle{\value{z}}}%
\put(-\value{x},-\value{y}){\circle{\value{z}}}%
\truex{500}\truey{1000}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% The following commands produce north-north-west arrows;
% the default length is 6700 units
% basic north-north-west arrow
\def\basicnnwar[#1]{\NNWAR{}{}{#100}}%
% north-north-west arrow
\newcommand{\nnwar}{\@ifnextchar[{\basicnnwar}{\basicnnwar[67]}}%
% basic north-north-west arrow with upper name
\def\basicNnwar[#1]#2{\NNWAR{#2}{}{#100}}%
% north-north-west arrow with upper name
\newcommand{\Nnwar}{\@ifnextchar[{\basicNnwar}{\basicNnwar[67]}}%
% basic north-north-west arrow with lower name
\def\basicnnwaR[#1]#2{\NNWAR{}{#2}{#100}}%
% north-north-west arrow with lower name
\newcommand{\nnwaR}{\@ifnextchar[{\basicnnwaR}{\basicnnwaR[67]}}%
% basic north-north-west distributor
\def\basicnnwdist[#1]{\NNWDIST{}{}{#100}}%
% north-north-west distributor
\newcommand{\nnwdist}{\@ifnextchar[{\basicnnwdist}{\basicnnwdist[67]}}%
% basic north-north-west distributor with upper name
\def\basicNnwdist[#1]#2{\NNWDIST{#2}{}{#100}}%
% north-north-west distributor with upper name
\newcommand{\Nnwdist}{\@ifnextchar[{\basicNnwdist}{\basicNnwdist[67]}}%
% basic north-north-west distributor with lower name
\def\basicnnwdisT[#1]#2{\NNWDIST{}{#2}{#100}}%
% north-north-west distributor with lower name
\newcommand{\nnwdisT}{\@ifnextchar[{\basicnnwdisT}{\basicnnwdisT[67]}}%
% basic north-north-west dotted arrow
\def\basicnnwdotar[#1]{\NNWDOTAR{}{}{#100}}%
% north-north-west dotted arrow
\newcommand{\nnwdotar}{\@ifnextchar[{\basicnnwdotar}{\basicnnwdotar[67]}}%
% basic north-north-west dotted arrow with upper name
\def\basicNnwdotar[#1]#2{\NNWDOTAR{#2}{}{#100}}%
% north-north-west dotted arrow with upper name
\newcommand{\Nnwdotar}{\@ifnextchar[{\basicNnwdotar}{\basicNnwdotar[67]}}%
% basic north-north-west dotted arrow with lower name
\def\basicnnwdotaR[#1]#2{\NNWDOTAR{}{#2}{#100}}%
% north-north-west dotted arrow with lower name
\newcommand{\nnwdotaR}{\@ifnextchar[{\basicnnwdotaR}{\basicnnwdotaR[67]}}%
% basic north-north-west monomorphism
\def\basicnnwmono[#1]{\NNWMONO{}{}{#100}}%
% north-north-west monomorphism
\newcommand{\nnwmono}{\@ifnextchar[{\basicnnwmono}{\basicnnwmono[67]}}%
% basic north-north-west monomorphism with upper name
\def\basicNnwmono[#1]#2{\NNWMONO{#2}{}{#100}}%
% north-north-west monomorphism with upper name
\newcommand{\Nnwmono}{\@ifnextchar[{\basicNnwmono}{\basicNnwmono[67]}}%
% basic north-north-west monomorphism with lower name
\def\basicnnwmonO[#1]#2{\NNWMONO{}{#2}{#100}}%
% north-north-west monomorphism with lower name
\newcommand{\nnwmonO}{\@ifnextchar[{\basicnnwmonO}{\basicnnwmonO[67]}}%
% basic north-north-west epimorphism
\def\basicnnwepi[#1]{\NNWEPI{}{}{#100}}%
% north-north-west epimorphism
\newcommand{\nnwepi}{\@ifnextchar[{\basicnnwepi}{\basicnnwepi[67]}}%
% basic north-north-west epimorphism with upper name
\def\basicNnwepi[#1]#2{\NNWEPI{#2}{}{#100}}%
% north-north-west epimorphism with upper name
\newcommand{\Nnwepi}{\@ifnextchar[{\basicNnwepi}{\basicNnwepi[67]}}%
% basic north-north-west epimorphism with lower name
\def\basicnnwepI[#1]#2{\NNWEPI{}{#2}{#100}}%
% north-north-west epimorphism with lower name
\newcommand{\nnwepI}{\@ifnextchar[{\basicnnwepI}{\basicnnwepI[67]}}%
% basic north-north-west bimorphism
\def\basicnnwbimo[#1]{\NNWBIMO{}{}{#100}}%
% north-north-west bimorphism
\newcommand{\nnwbimo}{\@ifnextchar[{\basicnnwbimo}{\basicnnwbimo[67]}}%
% basic north-north-west bimorphism with upper name
\def\basicNnwbimo[#1]#2{\NNWBIMO{#2}{}{#100}}%
% north-north-west bimorphism with upper name
\newcommand{\Nnwbimo}{\@ifnextchar[{\basicNnwbimo}{\basicNnwbimo[67]}}%
% basic north-north-west bimorphism with lower name
\def\basicnnwbimO[#1]#2{\NNWBIMO{}{#2}{#100}}%
% north-north-west bimorphism with lower name
\newcommand{\nnwbimO}{\@ifnextchar[{\basicnnwbimO}{\basicnnwbimO[67]}}%
% basic north-north-west isomorphism
\def\basicnnwiso[#1]{\NNWAR{\cong}{}{#100}}%
% north-north-west isomorphism
\newcommand{\nnwiso}{\@ifnextchar[{\basicnnwiso}{\basicnnwiso[67]}}%
% basic north-north-west isomorphism with upper name
\def\basicNnwiso[#1]#2{\NNWAR{#2}{\cong}{#100}}%
% north-north-west isomorphism with upper name
\newcommand{\Nnwiso}{\@ifnextchar[{\basicNnwiso}{\basicNnwiso[67]}}%
% basic north-north-west isomorphism with lower name
\def\basicnnwisO[#1]#2{\NNWAR{\cong}{#2}{#100}}%
% north-north-west isomorphism with lower name
\newcommand{\nnwisO}{\@ifnextchar[{\basicnnwisO}{\basicnnwisO[67]}}%
% north-north-west equality
\let\nnweql=\sseeql%
% north-north-west equality with upper name
\let\Nnweql=\Sseeql%
% north-north-west equality with lower name
\let\nnweqL=\sseeqL%
% basic north-north-east pair of arrows
\def\basicnnwbiar[#1]{\NNWBIAR{}{}{#100}}%
% north-north-east pair of arrows
\newcommand{\nnwbiar}{\@ifnextchar[{\basicnnwbiar}{\basicnnwbiar[67]}}%
% basic north-north-east pair of arrows with names
\def\basicNnwbiar[#1]#2#3{\NNWBIAR{#2}{#3}{#100}}%
% north-north-east pair of arrows with names
\newcommand{\Nnwbiar}{\@ifnextchar[{\basicNnwbiar}{\basicNnwbiar[67]}}%
\let\nnwbiaR=\Nnwbiar
% basic north-north-east pair of distributors
\def\basicnnwbidist[#1]{\NNWBIDIST{}{}{#100}}%
% north-north-east pair of distributors
\newcommand{\nnwbidist}{\@ifnextchar[{\basicnnwbidist}{\basicnnwbidist[67]}}%
% basic north-north-east pair of distributors with names
\def\basicNnwbidist[#1]#2#3{\NNWBIDIST{#2}{#3}{#100}}%
% north-north-east pair of distributors with names
\newcommand{\Nnwbidist}{\@ifnextchar[{\basicNnwbidist}{\basicNnwbidist[67]}}%
\let\nnwbidisT=\Nnwbidist
% basic north-north-east pair of adjoint arrows
\def\basicnnwadjar[#1]{\NNWADJAR{}{}{#100}}%
% north-north-east pair of adjoint arrows
\newcommand{\nnwadjar}{\@ifnextchar[{\basicnnwadjar}{\basicnnwadjar[67]}}%
% basic north-north-east pair of adjoint arrows with names
\def\basicNnwadjar[#1]#2#3{\NNWADJAR{#2}{#3}{#100}}%
% north-north-east pair of adjoint arrows with names
\newcommand{\Nnwadjar}{\@ifnextchar[{\basicNnwadjar}{\basicNnwadjar[67]}}%
\let\nnwadjaR=\Nnwadjar
% basic north-north-east pair of adjoint distributors
\def\basicnnwadjdist[#1]{\NNWADJDIST{}{}{#100}}%
% north-north-east pair of adjoint distributors
\newcommand{\nnwadjdist}{\@ifnextchar[{\basicnnwadjdist}{\basicnnwadjdist[67]}}%
% basic north-north-east pair of adjoint distributors with names
\def\basicNnwadjdist[#1]#2#3{\NNWADJDIST{#2}{#3}{#100}}%
% north-north-east pair of adjoint distributors with names
\newcommand{\Nnwadjdist}{\@ifnextchar[{\basicNnwadjdist}{\basicNnwadjdist[67]}}%
\let\nnwadjdisT=\Nnwadjdist
% EAST-EAST-NORTH-EAST ARROWS
% default length: 21100 units
% \EENEAR{f}{g}{n} draws a east-east-north-east arrow with names f, g
% and length n units
\newcommand{\EENEAR}[3]{\testdiagrammode%
\Y=#3%
\divide \Y by 2%
\Z=\Y%
\divide \Z by 3%
\begin{picture}(0,0)%
\put(-\Y,-\Z){\line(3,1){#3}}%
\put(\Y,\Z){\eenehead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% basic east-east-north-east arrow
\def\basiceenear[#1]{\EENEAR{}{}{#100}}%
% east-east-north-east arrow
\newcommand{\eenear}{\@ifnextchar[{\basiceenear}{\basiceenear[211]}}%
% basic east-east-north-east arrow with upper name
\def\basicEenear[#1]#2{\EENEAR{#2}{}{#100}}%
% east-east-north-east arrow with upper name
\newcommand{\Eenear}{\@ifnextchar[{\basicEenear}{\basicEenear[211]}}%
% basic east-east-north-east arrow with lower name
\def\basiceeneaR[#1]#2{\EENEAR{}{#2}{#100}}%
% east-east-north-east arrow with lower name
\newcommand{\eeneaR}{\@ifnextchar[{\basiceeneaR}{\basiceeneaR[211]}}%
% EAST-EAST-SOUTH-EAST ARROWS
% default length: 21100 units
% \EESEAR{f}{g}{n} draws an east-east-south-east arrow with names f, g
% and length n units
\newcommand{\EESEAR}[3]{\testdiagrammode%
\Y=#3%
\divide \Y by 2%
\Z=\Y%
\divide \Z by 3%
\begin{picture}(0,0)%
\put(-\Y,\Z){\line(3,-1){#3}}%
\put(\Y,-\Z){\eesehead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% basic east-east-south-east arrow
\def\basiceesear[#1]{\EESEAR{}{}{#100}}%
% east-east-south-east arrow
\newcommand{\eesear}{\@ifnextchar[{\basiceesear}{\basiceesear[211]}}%
% basic east-east-south-east arrow with upper name
\def\basicEesear[#1]#2{\EESEAR{#2}{}{#100}}%
% east-east-south-east arrow with upper name
\newcommand{\Eesear}{\@ifnextchar[{\basicEesear}{\basicEesear[211]}}%
% basic east-east-south-east arrow with lower name
\def\basiceeseaR[#1]#2{\EESEAR{}{#2}{#100}}%
% east-east-south-east arrow with lower name
\newcommand{\eeseaR}{\@ifnextchar[{\basiceeseaR}{\basiceeseaR[211]}}%
% WEST-WEST-NORTH-WEST ARROWs
% default length: 21100 units
% \WWNWAR{f}{g}{n} draws a west-west-north-west arrow with names f, g
% and length n units
\newcommand{\WWNWAR}[3]{\testdiagrammode%
\Y=#3%
\divide \Y by 2%
\Z=\Y%
\divide \Z by 3%
\begin{picture}(0,0)%
\put(\Y,-\Z){\line(-3,1){#3}}%
\put(-\Y,\Z){\wwnwhead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% basic west-west-north-west arrow
\def\basicwwnwar[#1]{\WWNWAR{}{}{#100}}%
% west-west-north-west arrow
\newcommand{\wwnwar}{\@ifnextchar[{\basicwwnwar}{\basicwwnwar[211]}}%
% basic west-west-north-west arrow with upper name
\def\basicWwnwar[#1]#2{\WWNWAR{#2}{}{#100}}%
% west-west-north-west arrow with upper name
\newcommand{\Wwnwar}{\@ifnextchar[{\basicWwnwar}{\basicWwnwar[211]}}%
% basic west-west-north-west arrow with lower name
\def\basicwwnwaR[#1]#2{\WWNWAR{}{#2}{#100}}%
% west-west-north-west arrow with lower name
\newcommand{\wwnwaR}{\@ifnextchar[{\basicwwnwaR}{\basicwwnwaR[211]}}%
% WEST-WEST-SOUTH-WEST ARROWS
% default length: 21100 units
% \WWSWAR{f}{g} draws a west-west-south-west arrow with names f, g
\newcommand{\WWSWAR}[3]{\testdiagrammode%
\Y=#3%
\divide \Y by 2%
\Z=\Y%
\divide \Z by 3%
\begin{picture}(0,0)%
\put(\Y,\Z){\line(-3,-1){#3}}%
\put(-\Y,-\Z){\wwswhead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% basic west-west-south-west arrow
\def\basicwwswar[#1]{\WWSWAR{}{}{#100}}%
% west-west-south-west arrow
\newcommand{\wwswar}{\@ifnextchar[{\basicwwswar}{\basicwwswar[211]}}%
% basic west-west-south-west arrow with upper name
\def\basicWwswar[#1]#2{\WWSWAR{#2}{}{#100}}%
% west-west-south-west arrow with upper name
\newcommand{\Wwswar}{\@ifnextchar[{\basicWwswar}{\basicWwswar[211]}}%
% basic west-west-south-west arrow with lower name
\def\basicwwswaR[#1]#2{\WWSWAR{}{#2}{#100}}%
% west-west-south-west arrow with lower name
\newcommand{\wwswaR}{\@ifnextchar[{\basicwwswaR}{\basicwwswaR[211]}}%
% NORTH-NORTH-NORTH-EAST ARROWS
% default length: 7100 units
% \NNNEAR{f}{g}{n} draws a north-north-north-east arrow with names f, g
% and length n units
\newcommand{\NNNEAR}[3]{\testdiagrammode%
\Y=#3%
\divide \Y by 2%
\Z=\Y%
\multiply \Z by 3%
\begin{picture}(0,0)%
\put(-\Y,-\Z){\line(1,3){#3}}%
\put(\Y,\Z){\nnnehead}%
\truex{100}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{z}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% basic north-north-north-east arrow
\def\basicnnnear[#1]{\NNNEAR{}{}{#100}}%
% north-north-north-east arrow
\newcommand{\nnnear}{\@ifnextchar[{\basicnnnear}{\basicnnnear[71]}}%
% basic north-north-north-east arrow with upper name
\def\basicNnnear[#1]#2{\NNNEAR{#2}{}{#100}}%
% north-north-north-east arrow with upper name
\newcommand{\Nnnear}{\@ifnextchar[{\basicNnnear}{\basicNnnear[71]}}%
% basic north-north-north-east arrow with lower name
\def\basicnnneaR[#1]#2{\NNNEAR{}{#2}{#100}}%
% north-north-north-east arrow with lower name
\newcommand{\nnneaR}{\@ifnextchar[{\basicnnneaR}{\basicnnneaR[71]}}%
% SOUTH-SOUTH-SOUTH-WEST ARROWS
% default length: 7100 units
% \SSSWAR{f}{g}{n} draws a south-south-south-west arrow with names f, g
% and length n units
\newcommand{\SSSWAR}[3]{\testdiagrammode%
\Y=#3%
\divide \Y by 2%
\Z=\Y%
\multiply \Z by 3%
\begin{picture}(0,0)%
\put(\Y,\Z){\line(-1,-3){#3}}%
\put(-\Y,-\Z){\ssswhead}%
\truex{100}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{z}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% basic south-south-south-west arrow
\def\basicssswar[#1]{\SSSWAR{}{}{#100}}%
% south-south-south-west arrow
\newcommand{\ssswar}{\@ifnextchar[{\basicssswar}{\basicssswar[71]}}%
% basic south-south-south-west arrow with upper name
\def\basicSsswar[#1]#2{\SSSWAR{#2}{}{#100}}%
% south-south-south-west arrow with upper name
\newcommand{\Ssswar}{\@ifnextchar[{\basicSsswar}{\basicSsswar[71]}}%
% basic south-south-south-west arrow with lower name
\def\basicssswaR[#1]#2{\SSSWAR{}{#2}{#100}}%
% south-south-south-west arrow with lower name
\newcommand{\ssswaR}{\@ifnextchar[{\basicssswaR}{\basicssswaR[71]}}%
% SOUTH-SOUTH-SOUTH-EAST ARROWS
% default length: 7100 units
% \SSSEAR{f}{g}{n} draws a south-south-south-east arrow with names f, g
% and length n units
\newcommand{\SSSEAR}[3]{\testdiagrammode%
\Y=#3%
\divide \Y by 2%
\Z=\Y%
\multiply \Z by 3%
\begin{picture}(0,0)%
\put(-\Y,\Z){\line(1,-3){#3}}%
\put(\Y,-\Z){\sssehead}%
\truex{200}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{z}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% basic south-south-south-east arrow
\def\basicsssear[#1]{\SSSEAR{}{}{#100}}%
% south-south-south-east arrow
\newcommand{\sssear}{\@ifnextchar[{\basicsssear}{\basicsssear[71]}}%
% basic south-south-south-east arrow with upper name
\def\basicSssear[#1]#2{\SSSEAR{#2}{}{#100}}%
% south-south-south-east arrow with upper name
\newcommand{\Sssear}{\@ifnextchar[{\basicSssear}{\basicSssear[71]}}%
% basic south-south-south-east arrow with lower name
\def\basicssseaR[#1]#2{\SSSEAR{}{#2}{#100}}%
% south-south-south-east arrow with lower name
\newcommand{\ssseaR}{\@ifnextchar[{\basicssseaR}{\basicssseaR[71]}}%
% NORTH-NORTH-NORTH-WEST ARROWS
% default length: 7100 units
% \NNNWAR{f}{g}{n} draws a north-north-north-west arrow with names f, g
% and length n units
\newcommand{\NNNWAR}[3]{\testdiagrammode%
\Y=#3%
\divide \Y by 2%
\Z=\Y%
\multiply \Z by 3%
\begin{picture}(0,0)%
\put(\Y,-\Z){\line(-1,3){#3}}%
\put(-\Y,\Z){\nnnwhead}%
\truex{200}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{z}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% basic north-north-north-west arrow
\def\basicnnnwar[#1]{\NNNWAR{}{}{#100}}%
% north-north-north-west arrow
\newcommand{\nnnwar}{\@ifnextchar[{\basicnnnwar}{\basicnnnwar[71]}}%
% basic north-north-north-west arrow with upper name
\def\basicNnnwar[#1]#2{\NNNWAR{#2}{}{#100}}%
% north-north-north-west arrow with upper name
\newcommand{\Nnnwar}{\@ifnextchar[{\basicNnnwar}{\basicNnnwar[71]}}%
% basic north-north-north-west arrow with lower name
\def\basicnnnwaR[#1]#2{\NNNWAR{}{#2}{#100}}%
% north-north-north-west arrow with lower name
\newcommand{\nnnwaR}{\@ifnextchar[{\basicnnnwaR}{\basicnnnwaR[71]}}%
% NORTH-EAST-EAST-NORTH-EAST ARROWS
% default length: 21500 units
% \NEENEAR{f}{g}{n} draws a north-east-east-north-east arrow with names f, g
% and length n units
\newcommand{\NEENEAR}[3]{\testdiagrammode%
\Y=#3%
\divide \Y by 2%
\Z=#3%
\divide \Z by 3%
\begin{picture}(0,0)%
\put(-\Y,-\Z){\line(3,2){#3}}%
\put(\Y,\Z){\neenehead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% basic north-east-east-north-east arrow
\def\basicneenear[#1]{\NEENEAR{}{}{#100}}%
% north-east-east-north-east arrow
\newcommand{\neenear}{\@ifnextchar[{\basicneenear}{\basicneenear[215]}}%
% basic north-east-east-north-east arrow with upper name
\def\basicNeenear[#1]#2{\NEENEAR{#2}{}{#100}}%
% north-east-east-north-east arrow with upper name
\newcommand{\Neenear}{\@ifnextchar[{\basicNeenear}{\basicNeenear[215]}}%
% basic north-east-east-north-east arrow with lower name
\def\basicneeneaR[#1]#2{\NEENEAR{}{#2}{#100}}%
% north-east-east-north-east arrow with lower name
\newcommand{\neeneaR}{\@ifnextchar[{\basicneeneaR}{\basicneeneaR[215]}}%
% SOUTH-EAST-EAST-SOUTH-EAST ARROWS
% DEFAULT LENGTH: 21500 UNITS
% \SEESEAR{f}{g} draws an sout-east-east-south-east arrow with names f, g
% and length n units
\newcommand{\SEESEAR}[3]{\testdiagrammode%
\Y=#3%
\divide \Y by 2%
\Z=#3%
\divide \Z by 3%
\begin{picture}(0,0)%
\put(-\Y,\Z){\line(3,-2){#3}}%
\put(\Y,-\Z){\seesehead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% basic south-east-east-south-east arrow
\def\basicseesear[#1]{\SEESEAR{}{}{#100}}%
% south-east-east-south-east arrow
\newcommand{\seesear}{\@ifnextchar[{\basicseesear}{\basicseesear[215]}}%
% basic south-east-east-south-east arrow with upper name
\def\basicSeesear[#1]#2{\SEESEAR{#2}{}{#100}}%
% south-east-east-south-east arrow with upper name
\newcommand{\Seesear}{\@ifnextchar[{\basicSeesear}{\basicSeesear[215]}}%
% basic south-east-east-south-east arrow with lower name
\def\basicseeseaR[#1]#2{\SEESEAR{}{#2}{#100}}%
% south-east-east-south-east arrow with lower name
\newcommand{\seeseaR}{\@ifnextchar[{\basicseeseaR}{\basicseeseaR[215]}}%
% NORTH-WEST-WEST-NORTH-WEST ARROWS
% default length: 21500 units
% \NWWNWAR{f}{g}{n} draws a north-west-west-north-west arrow with names f, g
% and length n units
\newcommand{\NWWNWAR}[3]{\testdiagrammode%
\Y=#3%
\divide \Y by 2%
\Z=#3%
\divide \Z by 3%
\begin{picture}(0,0)%
\put(\Y,-\Z){\line(-3,2){#3}}%
\put(-\Y,\Z){\nwwnwhead}%
\truex{200}\truey{800}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{y}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% basic north-west-west-north-west arrow
\def\basicnwwnwar[#1]{\NWWNWAR{}{}{#100}}%
% north-west-west-north-west arrow
\newcommand{\nwwnwar}{\@ifnextchar[{\basicnwwnwar}{\basicnwwnwar[215]}}%
% basic north-west-west-north-west arrow with upper name
\def\basicNwwnwar[#1]#2{\NWWNWAR{#2}{}{#100}}%
% north-west-west-north-west arrow with upper name
\newcommand{\Nwwnwar}{\@ifnextchar[{\basicNwwnwar}{\basicNwwnwar[215]}}%
% basic north-west-west-north-west arrow with lower name
\def\basicnwwnwaR[#1]#2{\NWWNWAR{}{#2}{#100}}%
% north-west-west-north-west arrow with lower name
\newcommand{\nwwnwaR}{\@ifnextchar[{\basicnwwnwaR}{\basicnwwnwaR[215]}}%
% SOUTH-WEST-WEST-SOUTH-WEST ARROWS
% default length: 21500 units
% \SWWSWAR{f}{g}{n} draws a south-west-west-south-west arrow with names f, g
% and length n units
\newcommand{\SWWSWAR}[3]{\testdiagrammode%
\Y=#3%
\divide \Y by 2%
\Z=#3%
\divide \Z by 3%
\begin{picture}(0,0)%
\put(\Y,\Z){\line(-3,-2){#3}}%
\put(-\Y,-\Z){\swwswhead}%
\truex{200}\truey{800}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{y}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% basic south-west-west-south-west arrow
\def\basicswwswar[#1]{\SWWSWAR{}{}{#100}}%
% south-west-west-south-west arrow
\newcommand{\swwswar}{\@ifnextchar[{\basicswwswar}{\basicswwswar[215]}}%
% basic south-west-west-south-west arrow with upper name
\def\basicSwwswar[#1]#2{\SWWSWAR{#2}{}{#100}}%
% south-west-west-south-west arrow with upper name
\newcommand{\Swwswar}{\@ifnextchar[{\basicSwwswar}{\basicSwwswar[215]}}%
% basic south-west-west-south-west arrow with lower name
\def\basicswwswaR[#1]#2{\SWWSWAR{}{#2}{#100}}%
% south-west-west-south-west arrow with lower name
\newcommand{\swwswaR}{\@ifnextchar[{\basicswwswaR}{\basicswwswaR[215]}}%
% NORTH-EAST-NORTH-NORTH-EAST ARROWS
% default length 14300 units
% \NENNEAR{f}{g}{n} draws a north-east-north-north-east arrow with names f, g
% and length n units
\newcommand{\NENNEAR}[3]{\testdiagrammode%
\Y=#3%
\divide \Y by 2%
\Z=#3%
\multiply \Z by 3%
\divide \Z by 4%
\begin{picture}(0,0)%
\put(-\Y,-\Z){\line(2,3){#3}}%
\put(\Y,\Z){\nennehead}%
\truex{100}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{z}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% basic north-east-north-north-east arrow
\def\basicnennear[#1]{\NENNEAR{}{}{#100}}%
% north-east-north-north-east arrow
\newcommand{\nennear}{\@ifnextchar[{\basicnennear}{\basicnennear[143]}}%
% basic north-east-north-north-east arrow with upper name
\def\basicNennear[#1]#2{\NENNEAR{#2}{}{#100}}%
% north-east-north-north-east arrow with upper name
\newcommand{\Nennear}{\@ifnextchar[{\basicNennear}{\basicNennear[143]}}%
% basic north-east-north-north-east arrow with lower name
\def\basicnenneaR[#1]#2{\NENNEAR{}{#2}{#100}}%
% north-east-north-north-east arrow with lower name
\newcommand{\nenneaR}{\@ifnextchar[{\basicnenneaR}{\basicnenneaR[143]}}%
% SOUTH-WEST-SOUTH-SOUTH-WEST ARROWS
% default length: 14300 units
% \SWSSWAR{f}{g}{n} draws a south-west-south-south-west arrow with names f, g
% and length n units
\newcommand{\SWSSWAR}[3]{\testdiagrammode%
\Y=#3%
\divide \Y by 2%
\Z=#3%
\multiply \Z by 3%
\divide \Z by 4%
\begin{picture}(0,0)%
\put(\Y,\Z){\line(-2,-3){#3}}%
\put(-\Y,-\Z){\swsswhead}%
\truex{100}\truez{600}%
\put(-\value{x},\value{x}){\makebox(0,\value{z})[r]{${#1}$}}%
\put(\value{x},-\value{z}){\makebox(0,\value{z})[l]{${#2}$}}%
\end{picture}}%
% basic south-west-south-south-west arrow
\def\basicswsswar[#1]{\SWSSWAR{}{}{#100}}%
% south-west-south-south-west arrow
\newcommand{\swsswar}{\@ifnextchar[{\basicswsswar}{\basicswsswar[143]}}%
% basic south-west-south-south-west arrow with upper name
\def\basicSwsswar[#1]#2{\SWSSWAR{#2}{}{#100}}%
% south-west-south-south-west arrow with upper name
\newcommand{\Swsswar}{\@ifnextchar[{\basicSwsswar}{\basicSwsswar[143]}}%
% basic south-west-south-south-west arrow with lower name
\def\basicswsswaR[#1]#2{\SWSSWAR{}{#2}{#100}}%
% south-west-south-south-west arrow with lower name
\newcommand{\swsswaR}{\@ifnextchar[{\basicswsswaR}{\basicswsswaR[143]}}%
% SOUT-EAST-SOUTH-SOUTH-EAST ARROWS
% default length: 14300 units
% \SESSEAR{f}{g}{n} draws a south-east-south-south-east arrow with names f, g
% and length n units
\newcommand{\SESSEAR}[3]{\testdiagrammode%
\Y=#3%
\divide \Y by 2%
\Z=#3%
\multiply \Z by 3%
\divide \Z by 4%
\begin{picture}(0,0)%
\put(-\Y,\Z){\line(2,-3){#3}}%
\put(\Y,-\Z){\sessehead}%
\truex{200}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{z}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% basic south-east-south-south-east arrow
\def\basicsessear[#1]{\SESSEAR{}{}{#100}}%
% south-east-south-south-east arrow
\newcommand{\sessear}{\@ifnextchar[{\basicsessear}{\basicsessear[143]}}%
% basic south-east-south-south-east arrow with upper name
\def\basicSessear[#1]#2{\SESSEAR{#2}{}{#100}}%
% south-east-south-south-east arrow with upper name
\newcommand{\Sessear}{\@ifnextchar[{\basicSessear}{\basicSessear[143]}}%
% basic south-east-south-south-east arrow with lower name
\def\basicsesseaR[#1]#2{\SESSEAR{}{#2}{#100}}%
% south-east-south-south-east arrow with lower name
\newcommand{\sesseaR}{\@ifnextchar[{\basicsesseaR}{\basicsesseaR[143]}}%
% NORTH-WEST-NORTH-NORTH-WEST ARROWS
% default length: 14300 units
% \NWNNWAR{f}{g}{n} draws a north-west-north-north-west arrow with names f, g
% and length n units
\newcommand{\NWNNWAR}[3]{\testdiagrammode%
\Y=#3%
\divide \Y by 2%
\Z=#3%
\multiply \Z by 3%
\divide \Z by 4%
\begin{picture}(0,0)%
\put(\Y,-\Z){\line(-2,3){#3}}%
\put(-\Y,\Z){\nwnnwhead}%
\truex{200}\truez{600}%
\put(\value{x},\value{x}){\makebox(0,\value{z})[l]{${#1}$}}%
\put(-\value{x},-\value{z}){\makebox(0,\value{z})[r]{${#2}$}}%
\end{picture}}%
% basic north-west-north-north-west arrow
\def\basicnwnnwar[#1]{\NWNNWAR{}{}{#100}}%
% north-west-north-north-west arrow
\newcommand{\nwnnwar}{\@ifnextchar[{\basicnwnnwar}{\basicnwnnwar[143]}}%
% basic north-west-north-north-west arrow with upper name
\def\basicNwnnwar[#1]#2{\NWNNWAR{#2}{}{#100}}%
% north-west-north-north-west arrow with upper name
\newcommand{\Nwnnwar}{\@ifnextchar[{\basicNwnnwar}{\basicNwnnwar[143]}}%
% basic north-west-north-north-west arrow with lower name
\def\basicnwnnwaR[#1]#2{\NWNNWAR{}{#2}{#100}}%
% north-west-north-north-west arrow with lower name
\newcommand{\nwnnwaR}{\@ifnextchar[{\basicnwnnwaR}{\basicnwnnwaR[143]}}%
% HORIZONTAL CURVED ARROWS
% The following commands produce horizontal curved arrows
% default length: 160 units
% North\East curved arrow with name [1] and length [2]x100 units
\newcommand{\Necurve}[2]%
{\testdiagrammode\begin{picture}(0,0)%
\truex{1300}\truey{2000}\truez{200}%
\put(0,\value{x}){\oval(#200,\value{y})[t]}%
\put(0,\value{x}){\makebox(0,0){\begin{picture}(#200,0)%
\put(#200,0){\line(0,-1){\value{z}}}%
\put(#200,-\value{z}){\shead}%
\put(0,0){\line(0,-1){\value{z}}}\end{picture}}}%
\truex{2500}%
\put(0,\value{x}){\makebox(0,0)[b]{${#1}$}}%
\end{picture}}%
% basic north\east curved arrow
\def\basicnecurvar[#1]{\Necurve{}{#1}}
% north\east curved arrow
\newcommand{\necurvar}{\@ifnextchar[{\basicnecurvar}{\basicnecurvar[160]}}%
% basic north\east curved arrow with name
\def\basicNecurvar[#1]#2{\Necurve{#2}{#1}}%
% north\east curved arrow with name
\newcommand{\Necurvar}{\@ifnextchar[{\basicNecurvar}{\basicNecurvar[160]}}%
\let\necurvaR=\Necurvar
% North\West curved arrow with name [1] and length [2]x100 units
\newcommand{\Nwcurve}[2]%
{\testdiagrammode\begin{picture}(0,0)%
\truex{1300}\truey{2000}\truez{200}%
\put(0,\value{x}){\oval(#200,\value{y})[t]}%
\put(0,\value{x}){\makebox(0,0){\begin{picture}(#200,0)%
\put(#200,0){\line(0,-1){\value{z}}}%
\put(0,0){\line(0,-1){\value{z}}}%
\put(0,-\value{z}){\shead}%
\end{picture}}}%
\truex{2500}%
\put(0,\value{x}){\makebox(0,0)[b]{${#1}$}}%
\end{picture}}%
% basic north\west curved arrow
\def\basicnwcurvar[#1]{\Nwcurve{}{#1}}
% north\west curved arrow
\newcommand{\nwcurvar}{\@ifnextchar[{\basicnwcurvar}{\basicnwcurvar[160]}}%
% basic north\west curved arrow with name
\def\basicNwcurvar[#1]#2{\Nwcurve{#2}{#1}}%
% north\west curved arrow with name
\newcommand{\Nwcurvar}{\@ifnextchar[{\basicNwcurvar}{\basicNwcurvar[160]}}%
\let\nwcurvaR=\Nwcurvar
% South\East curved arrow with name [1] and length [2]x100 units
\newcommand{\Securve}[2]%
{\testdiagrammode\begin{picture}(0,0)%
\truex{1300}\truey{2000}\truez{200}%
\put(0,-\value{x}){\oval(#200,\value{y})[b]}%
\put(0,-\value{x}){\makebox(0,0){\begin{picture}(#200,0)%
\put(#200,0){\line(0,1){\value{z}}}%
\put(0,0){\line(0,1){\value{z}}}%
\put(#200,\value{z}){\nhead}%
\end{picture}}}%
\truex{2500}%
\put(0,-\value{x}){\makebox(0,0)[t]{${#1}$}}%
\end{picture}}%
% basic south\east curved arrow
\def\basicsecurvar[#1]{\Securve{}{#1}}
% south\east curved arrow
\newcommand{\securvar}{\@ifnextchar[{\basicsecurvar}{\basicsecurvar[160]}}%
% basic south\east curved arrow with name
\def\basicSecurvar[#1]#2{\Securve{#2}{#1}}%
% south\east curved arrow with name
\newcommand{\Securvar}{\@ifnextchar[{\basicSecurvar}{\basicSecurvar[160]}}%
\let\securvaR=\Securvar
% South\West curved arrow with name [1] and length [2]x100 units
\newcommand{\Swcurve}[2]%
{\testdiagrammode\begin{picture}(0,0)%
\truex{1300}\truey{2000}\truez{200}%
\put(0,-\value{x}){\oval(#200,\value{y})[b]}%
\put(0,-\value{x}){\makebox(0,0){\begin{picture}(#200,0)%
\put(#200,0){\line(0,1){\value{z}}}%
\put(0,0){\line(0,1){\value{z}}}%
\put(0,\value{z}){\nhead}%
\end{picture}}}%
\truex{2500}%
\put(0,-\value{x}){\makebox(0,0)[t]{${#1}$}}%
\end{picture}}%
% basic south\west curved arrow
\def\basicswcurvar[#1]{\Swcurve{}{#1}}
% south\west curved arrow
\newcommand{\swcurvar}{\@ifnextchar[{\basicswcurvar}{\basicswcurvar[160]}}%
% basic south\west curved arrow with name
\def\basicSwcurvar[#1]#2{\Swcurve{#2}{#1}}%
% south\west curved arrow with name
\newcommand{\Swcurvar}{\@ifnextchar[{\basicSwcurvar}{\basicSwcurvar[160]}}%
\let\swcurvaR=\Swcurvar
% VERTICAL CURVED ARROWS
% The following commands produce vertical curved arrows
% default length: 160pt
% East\South curved arrow with name [1] and length [2]x100 units
\newcommand{\Escurve}[2]%
{\testdiagrammode\begin{picture}(0,0)%
\truex{1400}\truey{2000}\truez{200}%
\put(\value{x},0){\oval(\value{y},#200)[r]}%
\put(\value{x},0){\makebox(0,0){\begin{picture}(0,#200)%
\put(0,0){\line(-1,0){\value{z}}}%
\put(0,#200){\line(-1,0){\value{z}}}%
\put(-\value{z},0){\whead}%
\end{picture}}}%
\truex{2500}%
\put(\value{x},0){\makebox(0,0)[l]{${#1}$}}%
\end{picture}}%
% basic east\south curved arrow
\def\basicescurvar[#1]{\Escurve{}{#1}}
% east\south curved arrow
\newcommand{\escurvar}{\@ifnextchar[{\basicescurvar}{\basicescurvar[160]}}%
% basic east\south curved arrow with name
\def\basicEscurvar[#1]#2{\Escurve{#2}{#1}}%
% east\south curved arrow with name
\newcommand{\Escurvar}{\@ifnextchar[{\basicEscurvar}{\basicEscurvar[160]}}%
\let\escurvaR=\Escurvar
% East\North curved arrow with name [1] and length [2]x100 units
\newcommand{\Encurve}[2]%
{\testdiagrammode\begin{picture}(0,0)%
\truex{1400}\truey{2000}\truez{200}%
\put(\value{x},0){\oval(\value{y},#200)[r]}%
\put(\value{x},0){\makebox(0,0){\begin{picture}(0,#200)%
\put(0,0){\line(-1,0){\value{z}}}%
\put(0,#200){\line(-1,0){\value{z}}}%
\put(-\value{z},#200){\whead}%
\end{picture}}}%
\truex{2500}%
\put(\value{x},0){\makebox(0,0)[l]{${#1}$}}%
\end{picture}}%
% basic east\north curved arrow
\def\basicencurvar[#1]{\Encurve{}{#1}}
% east\north curved arrow
\newcommand{\encurvar}{\@ifnextchar[{\basicencurvar}{\basicencurvar[160]}}%
% basic east\north curved arrow with name
\def\basicEncurvar[#1]#2{\Encurve{#2}{#1}}%
% east\north curved arrow with name
\newcommand{\Encurvar}{\@ifnextchar[{\basicEncurvar}{\basicEncurvar[160]}}%
\let\encurvaR=\Encurvar
% West\South curved arrow with name [1] and length [2]x100 units
\newcommand{\Wscurve}[2]%
{\testdiagrammode\begin{picture}(0,0)%
\truex{1300}\truey{2000}\truez{200}%
\put(-\value{x},0){\oval(\value{y},#200)[l]}%
\put(-\value{x},0){\makebox(0,0){\begin{picture}(0,#200)%
\put(0,0){\line(1,0){\value{z}}}%
\put(0,#200){\line(1,0){\value{z}}}%
\put(\value{z},0){\ehead}%
\end{picture}}}%
\truex{2400}%
\put(-\value{x},0){\makebox(0,0)[r]{${#1}$}}%
\end{picture}}%
% basic west\south curved arrow
\def\basicwscurvar[#1]{\Wscurve{}{#1}}
% west\south curved arrow
\newcommand{\wscurvar}{\@ifnextchar[{\basicwscurvar}{\basicwscurvar[160]}}%
% basic west\south curved arrow with name
\def\basicWscurvar[#1]#2{\Wscurve{#2}{#1}}%
% west\south curved arrow with name
\newcommand{\Wscurvar}{\@ifnextchar[{\basicWscurvar}{\basicWscurvar[160]}}%
\let\wscurvaR=\Wscurvar
% West\North curved arrow with name [1] and length [2]x100 units
\newcommand{\Wncurve}[2]%
{\testdiagrammode\begin{picture}(0,0)%
\truex{1300}\truey{2000}\truez{200}%
\put(-\value{x},0){\oval(\value{y},#200)[l]}%
\put(-\value{x},0){\makebox(0,0){\begin{picture}(0,#200)%
\put(0,0){\line(1,0){\value{z}}}%
\put(\value{z},#200){\ehead}%
\put(0,#200){\line(1,0){\value{z}}}%
\end{picture}}}%
\truex{2400}%
\put(-\value{x},0){\makebox(0,0)[r]{${#1}$}}%
\end{picture}}%
% basic west\north curved arrow
\def\basicwncurvar[#1]{\Wncurve{}{#1}}
% west\north curved arrow
\newcommand{\wncurvar}{\@ifnextchar[{\basicwncurvar}{\basicwncurvar[160]}}%
% basic west\north curved arrow with name
\def\basicWncurvar[#1]#2{\Wncurve{#2}{#1}}%
% west\north curved arrow with name
\newcommand{\Wncurvar}{\@ifnextchar[{\basicWncurvar}{\basicWncurvar[160]}}%
\let\wncurvaR=\Wncurvar
\catcode`\@=12