% This should appear in a file named diagram.tex

% This should appear in a file named diagram.tex
% Copyright 1988,1989 Michael Barr
% Department of Mathematics and Statistics
% McGill University
% 805 Sherbrooke St., W
% Montreal, Quebec, Canada
% H3P 1S4
%
% [email protected]
%
% All commercial rights reserved. May be freely distributed
% and used with the following exceptions:
% 1. No commercial use without explicit permission.
% 2. It may not be used by any employee of a telephone
% company.
% 3. It may not be distributed without this notice.
%
% Last revised 91-05-04

% Ascii character test:
% 32: 33: ! 34: " 35: # 36: $ 37: % 38: & 39: '
% 40: ( 41: ) 42: * 43: + 44: , 45: - 46: . 47: /
% 48: 0 49: 1 50: 2 51: 3 52: 4 53: 5 54: 6 55: 7
% 56: 8 57: 9 58: : 59: ; 60: < 61: = 62: > 63: ?
% 64: @ 65: A 66: B 67: C 68: D 69: E 70: F 71: G
% 72: H 73: I 74: J 75: K 76: L 77: M 78: N 79: O
% 80: P 81: Q 82: R 83: S 84: T 85: U 86: V 87: W
% 88: X 89: Y 90: Z 91: [ 92: \ 93: ] 94: ^ 95: _
% 96: ` 97: a 98: b 99: c 100: d 101: e 102: f 103: g
% 104: h 105: i 106: j 107: k 108: l 109: m 110: n 111: o
% 112: p 113: q 114: r 115: s 116: t 117: u 118: v 119: w
% 120: x 121: y 122: z 123: { 124: | 125: } 126: ~

\makeatletter

\def\diagram{\m@th\leftwidth=\z@ \rightwidth=\z@ \topheight=\z@
\botheight=\z@ \setbox\@picbox\hbox\bgroup}

\def\enddiagram{\egroup\wd\@picbox\rightwidth\unitlength
\ht\@picbox\topheight\unitlength \dp\@picbox\botheight\unitlength
\hskip\leftwidth\unitlength\box\@picbox}

\def\bfig{\begin{diagram}}
\def\efig{\end{diagram}}
\newcount\wideness \newcount\leftwidth \newcount\rightwidth
\newcount\highness \newcount\topheight \newcount\botheight

\def\ratchet#1#2{\ifnum#1<#2 \global #1=#2 \fi}

\def\putbox(#1,#2)#3{%
\horsize{\wideness}{#3} \divide\wideness by 2
{\advance\wideness by #1 \ratchet{\rightwidth}{\wideness}}
{\advance\wideness by -#1 \ratchet{\leftwidth}{\wideness}}
\vertsize{\highness}{#3} \divide\highness by 2
{\advance\highness by #2 \ratchet{\topheight}{\highness}}
{\advance\highness by -#2 \ratchet{\botheight}{\highness}}
\put(#1,#2){\makebox(0,0){$#3$}}}

\def\putlbox(#1,#2)#3{%
\horsize{\wideness}{#3}
{\advance\wideness by #1 \ratchet{\rightwidth}{\wideness}}
{\ratchet{\leftwidth}{-#1}}
\vertsize{\highness}{#3} \divide\highness by 2
{\advance\highness by #2 \ratchet{\topheight}{\highness}}
{\advance\highness by -#2 \ratchet{\botheight}{\highness}}
\put(#1,#2){\makebox(0,0)[l]{$#3$}}}

\def\putrbox(#1,#2)#3{%
\horsize{\wideness}{#3}
{\ratchet{\rightwidth}{#1}}
{\advance\wideness by -#1 \ratchet{\leftwidth}{\wideness}}
\vertsize{\highness}{#3} \divide\highness by 2
{\advance\highness by #2 \ratchet{\topheight}{\highness}}
{\advance\highness by -#2 \ratchet{\botheight}{\highness}}
\put(#1,#2){\makebox(0,0)[r]{$#3$}}}

\def\adjust[#1]{} % For compatibility

\newcount \coefa
\newcount \coefb
\newcount \coefc
\newcount\tempcounta
\newcount\tempcountb
\newcount\tempcountc
\newcount\tempcountd
\newcount\xext
\newcount\yext
\newcount\xoff
\newcount\yoff
\newcount\gap%
\newcount\arrowtypea
\newcount\arrowtypeb
\newcount\arrowtypec
\newcount\arrowtyped
\newcount\arrowtypee
\newcount\height
\newcount\width
\newcount\xpos
\newcount\ypos
\newcount\run
\newcount\rise
\newcount\arrowlength
\newcount\halflength
\newcount\arrowtype
\newdimen\tempdimen
\newdimen\xlen
\newdimen\ylen
\newsavebox{\tempboxa}%
\newsavebox{\tempboxb}%
\newsavebox{\tempboxc}%

\newdimen\w@dth

\def\setw@dth#1#2{\setbox\z@\hbox{\m@th$#1$}\w@dth=\wd\z@
\setbox\@ne\hbox{\m@th$#2$}\ifnum\w@dth<\wd\@ne \w@dth=\wd\@ne \fi
\advance\w@dth by 1.2em}

%The definitions below look more elaborate than they need to be.
%The reason is that an empty asscript will still cause extra vertical
%spacing and the only way to avoid ugly extra space seems to be using
%some such method as this.

\def\t@^#1_#2{\allowbreak\def\n@one{#1}\def\n@two{#2}\mathrel
{\setw@dth{#1}{#2}
\mathop{\hbox to \w@dth{\rightarrowfill}}\limits
\ifx\n@one\empty\else ^{\box\z@}\fi
\ifx\n@two\empty\else _{\box\@ne}\fi}}
%\def\t@^#1_#2{\mathrel{\mathop{\hbox{\rightarrowfill}}\limits
%^{\mkern12mu#1\mkern12mu}_{\mkern12mu#2\mkern12mu}}}
\def\t@@^#1{\@ifnextchar_{\t@^{#1}}{\t@^{#1}_{}}}
\def\to{\@ifnextchar^{\t@@}{\t@@^{}}}

\def\t@left^#1_#2{\def\n@one{#1}\def\n@two{#2}\mathrel{\setw@dth{#1}{#2}
\mathop{\hbox to \w@dth{\leftarrowfill}}\limits
\ifx\n@one\empty\else ^{\box\z@}\fi
\ifx\n@two\empty\else _{\box\@ne}\fi}}
%\def\t@left^#1_#2{\mathrel{\mathop{\hbox{\leftarrowfill}}\limits
%^{\mkern12mu#1\mkern12mu}_{\mkern12mu#2\mkern12mu}}}
\def\t@@left^#1{\@ifnextchar_{\t@left^{#1}}{\t@left^{#1}_{}}}
\def\toleft{\@ifnextchar^{\t@@left}{\t@@left^{}}}

\def\two@^#1_#2{\allowbreak
\def\n@one{#1}\def\n@two{#2}\mathrel{\setw@dth{#1}{#2}
\mathop{\vcenter{\lineskip\z@\baselineskip\z@
\hbox to \w@dth{\rightarrowfill}%
\hbox to \w@dth{\rightarrowfill}}%
}\limits
\ifx\n@one\empty\else ^{\box\z@}\fi
\ifx\n@two\empty\else _{\box\@ne}\fi}}
\def\tw@@^#1{\@ifnextchar _{\two@^{#1}}{\two@^{#1}_{}}}
\def\two{\@ifnextchar ^{\tw@@}{\tw@@^{}}}

\def\tofr@^#1_#2{\def\n@one{#1}\def\n@two{#2}\mathrel{\setw@dth{#1}{#2}
\mathop{\vcenter{\hbox to \w@dth{\rightarrowfill}\kern-1.7ex
\hbox to \w@dth{\leftarrowfill}}%
}\limits
\ifx\n@one\empty\else ^{\box\z@}\fi
\ifx\n@two\empty\else _{\box\@ne}\fi}}
\def\t@fr@^#1{\@ifnextchar_ {\tofr@^{#1}}{\tofr@^{#1}_{}}}
\def\tofro{\@ifnextchar^ {\t@fr@}{\t@fr@^{}}}

\def\epi{\mathop{\mathchar"221\mkern -12mu\mathchar"221}\limits}
\def\leftepi{\mathop{\mathchar"220\mkern -12mu\mathchar"220}\limits}
\def\mon{\mathop{\m@th\hbox to
14.6\P@{\lasyb\char'51\hskip-2.1\P@$\arrext$\hss
$\mathord\rightarrow$}}\limits} % width of \epi
\def\leftmono{\mathrel{\m@th\hbox to
14.6\P@{$\mathord\leftarrow$\hss$\arrext$\hskip-2.1\P@\lasyb\char'50%
}}\limits} % width of \epi
\mathchardef\arrext="0200 % amr minus for arrow extension (see \into)

\setlength{\unitlength}{.01em}%
\def\settypes(#1,#2,#3){\arrowtypea#1 \arrowtypeb#2 \arrowtypec#3}
\def\settoheight#1#2{\setbox\@tempboxa\hbox{#2}#1\ht\@tempboxa\relax}%
\def\settodepth#1#2{\setbox\@tempboxa\hbox{#2}#1\dp\@tempboxa\relax}%
\def\settokens`#1`#2`#3`#4`{%
\def\tokena{#1}\def\tokenb{#2}\def\tokenc{#3}\def\tokend{#4}}
\def\setsqparms[#1`#2`#3`#4;#5`#6]{%
\arrowtypea #1
\arrowtypeb #2
\arrowtypec #3
\arrowtyped #4
\width #5
\height #6
}
\def\setpos(#1,#2){\xpos=#1 \ypos#2}

\def\settriparms[#1`#2`#3;#4]{\settripairparms[#1`#2`#3`1`1;#4]}%

\def\settripairparms[#1`#2`#3`#4`#5;#6]{%
\arrowtypea #1
\arrowtypeb #2
\arrowtypec #3
\arrowtyped #4
\arrowtypee #5
\width #6
\height #6
}

\def\resetparms{\settripairparms[1`1`1`1`1;500]\width 500}%default values%

\resetparms

\def\mvector(#1,#2)#3{%%
\put(0,0){\vector(#1,#2){#3}}%
\put(0,0){\vector(#1,#2){26}}%
}
\def\evector(#1,#2)#3{{%%
\arrowlength #3
\put(0,0){\vector(#1,#2){\arrowlength}}%
\advance \arrowlength by-30
\put(0,0){\vector(#1,#2){\arrowlength}}%
}}

\def\horsize#1#2{%
\settowidth{\tempdimen}{$#2$}%
#1=\tempdimen
\divide #1 by\unitlength
}

\def\vertsize#1#2{%
\settoheight{\tempdimen}{$#2$}%
#1=\tempdimen
\settodepth{\tempdimen}{$#2$}%
\advance #1 by\tempdimen
\divide #1 by\unitlength
}

\def\putvector(#1,#2)(#3,#4)#5#6{{%
\ifnum3<\arrowtype
\putdashvector(#1,#2)(#3,#4)#5\arrowtype
\else
\ifnum\arrowtype<-3
\putdashvector(#1,#2)(#3,#4)#5\arrowtype
\else
\xpos=#1
\ypos=#2
\run=#3
\rise=#4
\arrowlength=#5
\ifnum \arrowtype<0
\ifnum \run=0
\advance \ypos by-\arrowlength
\else
\tempcounta \arrowlength
\multiply \tempcounta by\rise
\divide \tempcounta by\run
\ifnum\run>0
\advance \xpos by\arrowlength
\advance \ypos by\tempcounta
\else
\advance \xpos by-\arrowlength
\advance \ypos by-\tempcounta
\fi
\fi
\multiply \arrowtype by-1
\multiply \rise by-1
\multiply \run by-1
\fi
\ifcase \arrowtype
\or \put(\xpos,\ypos){\vector(\run,\rise){\arrowlength}}%
\or \put(\xpos,\ypos){\mvector(\run,\rise)\arrowlength}%
\or \put(\xpos,\ypos){\evector(\run,\rise){\arrowlength}}%
\fi\fi\fi
}}

\def\putsplitvector(#1,#2)#3#4{%%
\xpos #1
\ypos #2
\arrowtype #4
\halflength #3
\arrowlength #3
\gap 140
\advance \halflength by-\gap
\divide \halflength by2
\ifnum\arrowtype>0
\ifcase \arrowtype
\or \put(\xpos,\ypos){\line(0,-1){\halflength}}%
\advance\ypos by-\halflength
\advance\ypos by-\gap
\put(\xpos,\ypos){\vector(0,-1){\halflength}}%
\or \put(\xpos,\ypos){\line(0,-1)\halflength}%
\put(\xpos,\ypos){\vector(0,-1)3}%
\advance\ypos by-\halflength
\advance\ypos by-\gap
\put(\xpos,\ypos){\vector(0,-1){\halflength}}%
\or \put(\xpos,\ypos){\line(0,-1)\halflength}%
\advance\ypos by-\halflength
\advance\ypos by-\gap
\put(\xpos,\ypos){\evector(0,-1){\halflength}}%
\fi
\else \arrowtype=-\arrowtype
\ifcase\arrowtype
\or \advance \ypos by-\arrowlength
\put(\xpos,\ypos){\line(0,1){\halflength}}%
\advance\ypos by\halflength
\advance\ypos by\gap
\put(\xpos,\ypos){\vector(0,1){\halflength}}%
\or \advance \ypos by-\arrowlength
\put(\xpos,\ypos){\line(0,1)\halflength}%
\put(\xpos,\ypos){\vector(0,1)3}%
\advance\ypos by\halflength
\advance\ypos by\gap
\put(\xpos,\ypos){\vector(0,1){\halflength}}%
\or \advance \ypos by-\arrowlength
\put(\xpos,\ypos){\line(0,1)\halflength}%
\advance\ypos by\halflength
\advance\ypos by\gap
\put(\xpos,\ypos){\evector(0,1){\halflength}}%
\fi
\fi
}

\def\putmorphism(#1)(#2,#3)[#4`#5`#6]#7#8#9{{%
\run #2
\rise #3
\ifnum\rise=0
\puthmorphism(#1)[#4`#5`#6]{#7}{#8}#9%
\else\ifnum\run=0
\putvmorphism(#1)[#4`#5`#6]{#7}{#8}#9%
\else
\setpos(#1)%
\arrowlength #7
\arrowtype #8
\ifnum\run=0
\else\ifnum\rise=0
\else
\ifnum\run>0
\coefa=1
\else
\coefa=-1
\fi
\ifnum\arrowtype>0
\coefb=0
\coefc=-1
\else
\coefb=\coefa
\coefc=1
\arrowtype=-\arrowtype
\fi
\width=2
\multiply \width by\run
\divide \width by\rise
\ifnum \width<0 \width=-\width\fi
\advance\width by60
\if l#9 \width=-\width\fi
\putbox(\xpos,\ypos){#4}% %node 1
{\multiply \coefa by\arrowlength% %node 2
\advance\xpos by\coefa
\multiply \coefa by\rise
\divide \coefa by\run
\advance \ypos by\coefa
\putbox(\xpos,\ypos){#5} }%
{\multiply \coefa by\arrowlength% %label
\divide \coefa by2
\advance \xpos by\coefa
\advance \xpos by\width
\multiply \coefa by\rise
\divide \coefa by\run
\advance \ypos by\coefa
\if l#9%
\putrbox(\xpos,\ypos){#6}%
\else\if r#9%
\putlbox(\xpos,\ypos){#6}%
\fi\fi }%
{\multiply \rise by-\coefc% %arrow
\multiply \run by-\coefc
\multiply \coefb by\arrowlength
\advance \xpos by\coefb
\multiply \coefb by\rise
\divide \coefb by\run
\advance \ypos by\coefb
\multiply \coefc by70
\advance \ypos by\coefc
\multiply \coefc by\run
\divide \coefc by\rise
\advance \xpos by\coefc
\multiply \coefa by140
\multiply \coefa by\run
\divide \coefa by\rise
\advance \arrowlength by\coefa
\ifcase\arrowtype
\or \put(\xpos,\ypos){\vector(\run,\rise){\arrowlength}}%
\or \put(\xpos,\ypos){\mvector(\run,\rise){\arrowlength}}%
\or \put(\xpos,\ypos){\evector(\run,\rise){\arrowlength}}%
\fi}\fi\fi\fi\fi}}

\newcount\numbdashes \newcount\lengthdash \newcount\increment

\def\howmanydashes{% Actually returns both number and length
\numbdashes=\arrowlength \lengthdash=40
\divide\numbdashes by \lengthdash
\lengthdash=\arrowlength
\divide\lengthdash by \numbdashes
%This futzing around is to minimize round-off error.
\increment=\lengthdash
\multiply\lengthdash by 3
\divide\lengthdash by 5
}

\def\putdashvector(#1)(#2,#3)#4#5{%
\ifnum#3=0 \putdashhvector(#1){#4}#5
\else
\ifnum#2=0
\putdashvvector(#1){#4}#5\fi\fi}

\def\putdashhvector(#1,#2)#3#4{{%
\arrowlength=#3 \howmanydashes
\multiput(#1,#2)(\increment,0){\numbdashes}%
{\vrule height .4pt width \lengthdash\unitlength}
\arrowtype=#4 \xpos=#1
\ifnum\arrowtype<0 \advance\arrowtype by 7 \fi
\ifcase\arrowtype
\or \advance\xpos by 10
\put(\xpos,#2){\vector(-1,0){\lengthdash}}
\advance\xpos by 40
\put(\xpos,#2){\vector(-1,0){\lengthdash}}
\or \advance \xpos by 10
\put(\xpos,#2){\vector(-1,0){\lengthdash}}
\advance\xpos by \arrowlength
\advance\xpos by -50
\put(\xpos,#2){\vector(-1,0){\lengthdash}}
\or \advance\xpos by 10
\put(\xpos,#2){\vector(-1,0){\lengthdash}}
\or \advance\xpos by \arrowlength
\advance\xpos by -\lengthdash
\put(\xpos,#2){\vector(1,0){\lengthdash}}
\or {\advance\xpos by 10
\put(\xpos,#2){\vector(1,0){\lengthdash}}}
\advance\xpos by \arrowlength
\advance\xpos by -\lengthdash
\put(\xpos,#2){\vector(1,0){\lengthdash}}
\or \advance\xpos by \arrowlength
\advance\xpos by -\lengthdash
\put(\xpos,#2){\vector(1,0){\lengthdash}}
\advance\xpos by -40
\put(\xpos,#2){\vector(1,0){\lengthdash}}
\fi
}}

\def\putdashvvector(#1,#2)#3#4{{%
\arrowlength=#3 \howmanydashes
\ypos=#2 \advance\ypos by -\arrowlength
\multiput(#1,#2)(0,\increment){\numbdashes}%
{\vrule width .4pt height \lengthdash\unitlength}
\arrowtype=#4 \ypos=#2
\ifnum\arrowtype<0 \advance\arrowtype by 7 \fi
\ifcase\arrowtype
\or \advance\ypos by \arrowlength \advance\ypos by -40
\put(#1,\ypos){\vector(0,1){\lengthdash}}
\advance\ypos by -40
\put(#1,\ypos){\vector(0,1){\lengthdash}}
\or \advance\ypos by 10
\put(#1,\ypos){\vector(0,1){\lengthdash}}
\advance\ypos by \arrowlength \advance\ypos by -40
\put(#1,\ypos){\vector(0,1){\lengthdash}}
\or \advance\ypos by \arrowlength \advance\ypos by -40
\put(#1,\ypos){\vector(0,1){\lengthdash}}
\or \advance\ypos by 10
\put(#1,\ypos){\vector(0,-1){\lengthdash}}
\or \advance\ypos by 10
\put(#1,\ypos){\vector(0,-1){\lengthdash}}
\advance\ypos by \arrowlength \advance\ypos by -40
\put(#1,\ypos){\vector(0,-1){\lengthdash}}
\or \advance\ypos by 10
\put(#1,\ypos){\vector(0,-1){\lengthdash}}
\advance\ypos by 40
\put(#1,\ypos){\vector(0,-1){\lengthdash}}
\fi
}}

\def\puthmorphism(#1,#2)[#3`#4`#5]#6#7#8{{%
\xpos #1
\ypos #2
\width #6
\arrowlength #6
\arrowtype=#7
\putbox(\xpos,\ypos){#3\vphantom{#4}}%
{\advance \xpos by\arrowlength
\putbox(\xpos,\ypos){\vphantom{#3}#4}}%
\horsize{\tempcounta}{#3}%
\horsize{\tempcountb}{#4}%
\divide \tempcounta by2
\divide \tempcountb by2
\advance \tempcounta by30
\advance \tempcountb by30
\advance \xpos by\tempcounta
\advance \arrowlength by-\tempcounta
\advance \arrowlength by-\tempcountb
\putvector(\xpos,\ypos)(1,0)\arrowlength\arrowtype
\divide \arrowlength by2
\advance \xpos by\arrowlength
\vertsize{\tempcounta}{#5}%
\divide\tempcounta by2
\advance \tempcounta by20
\if a#8 %
\advance \ypos by\tempcounta
\putbox(\xpos,\ypos){#5}%
\else
\advance \ypos by-\tempcounta
\putbox(\xpos,\ypos){#5}%
\fi}}

\def\putvmorphism(#1,#2)[#3`#4`#5]#6#7#8{{%
\xpos #1
\ypos #2
\arrowlength #6
\arrowtype #7
\settowidth{\xlen}{$#5$}%
\putbox(\xpos,\ypos){#3}%
{\advance \ypos by-\arrowlength
\putbox(\xpos,\ypos){#4}}%
{\advance\arrowlength by-140
\advance \ypos by-70
\ifdim\xlen>0pt
\if m#8%
\putsplitvector(\xpos,\ypos)\arrowlength\arrowtype
\else
\putvector(\xpos,\ypos)(0,-1)\arrowlength\arrowtype
\fi
\else
\putvector(\xpos,\ypos)(0,-1)\arrowlength\arrowtype
\fi}%
\ifdim\xlen>0pt
\divide \arrowlength by2
\advance\ypos by-\arrowlength
\if l#8%
\advance \xpos by-40
\putrbox(\xpos,\ypos){#5}%
\else\if r#8%
\advance \xpos by40
\putlbox(\xpos,\ypos){#5}%
\else
\putbox(\xpos,\ypos){#5}%
\fi\fi
\fi
}}

\def\putsquarep<#1>(#2)[#3;#4`#5`#6`#7]{{%
\setsqparms[#1]%
\setpos(#2)%
\settokens`#3`%
\puthmorphism(\xpos,\ypos)[\tokenc`\tokend`{#7}]{\width}{\arrowtyped}b%
\advance\ypos by \height
\puthmorphism(\xpos,\ypos)[\tokena`\tokenb`{#4}]{\width}{\arrowtypea}a%
\putvmorphism(\xpos,\ypos)[``{#5}]{\height}{\arrowtypeb}l%
\advance\xpos by \width
\putvmorphism(\xpos,\ypos)[``{#6}]{\height}{\arrowtypec}r%
}}

\def\putsquare{\@ifnextchar <{\putsquarep}{\putsquarep%
<\arrowtypea`\arrowtypeb`\arrowtypec`\arrowtyped;\width`\height>}}
\def\square{\@ifnextchar< {\squarep}{\squarep
<\arrowtypea`\arrowtypeb`\arrowtypec`\arrowtyped;\width`\height>}}
% #6
\def\squarep<#1>[#2`#3`#4`#5;#6`#7`#8`#9]{{% % #2------>#3
\setsqparms[#1]% % | |
\diagram% % | |
\putsquarep<\arrowtypea`\arrowtypeb`\arrowtypec`% % #7| |#8
\arrowtyped;\width`\height>% % | |
(0,0)[#2`#3`#4`{#5};#6`#7`#8`{#9}]% % | |
\enddiagram% % v v
}} % #4------>#5
% #9
\def\putptrianglep<#1>(#2,#3)[#4`#5`#6;#7`#8`#9]{{%
\settriparms[#1]%
\xpos=#2 \ypos=#3
\advance\ypos by \height
\puthmorphism(\xpos,\ypos)[#4`#5`{#7}]{\height}{\arrowtypea}a%
\putvmorphism(\xpos,\ypos)[`#6`{#8}]{\height}{\arrowtypeb}l%
\advance\xpos by\height
\putmorphism(\xpos,\ypos)(-1,-1)[``{#9}]{\height}{\arrowtypec}r%
}}

\def\putptriangle{\@ifnextchar <{\putptrianglep}{\putptrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
\def\ptriangle{\@ifnextchar <{\ptrianglep}{\ptrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
% #5
\def\ptrianglep<#1>[#2`#3`#4;#5`#6`#7]{{%% % #2----->#3
\settriparms[#1]% % | /
\diagram% % | /
\putptrianglep<\arrowtypea`\arrowtypeb`% % #6| /#7
\arrowtypec;\height>% % | /
(0,0)[#2`#3`#4;#5`#6`{#7}]% % | /
\enddiagram%% % v v
}} % #4

\def\putqtrianglep<#1>(#2,#3)[#4`#5`#6;#7`#8`#9]{{%
\settriparms[#1]%
\xpos=#2 \ypos=#3
\advance\ypos by\height
\puthmorphism(\xpos,\ypos)[#4`#5`{#7}]{\height}{\arrowtypea}a%
\putmorphism(\xpos,\ypos)(1,-1)[``{#8}]{\height}{\arrowtypeb}l%
\advance\xpos by\height
\putvmorphism(\xpos,\ypos)[`#6`{#9}]{\height}{\arrowtypec}r%
}}

\def\putqtriangle{\@ifnextchar <{\putqtrianglep}{\putqtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
\def\qtriangle{\@ifnextchar <{\qtrianglep}{\qtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
% #5
\def\qtrianglep<#1>[#2`#3`#4;#5`#6`#7]{{%% % #2----->#3
\settriparms[#1]% % \ |
\width=\height % \ |
\diagram% % #6\ |#7
\putqtrianglep<\arrowtypea`\arrowtypeb`% % \ |
\arrowtypec;\height>% % \ |
(0,0)[#2`#3`#4;#5`#6`{#7}]% % v v
\enddiagram%% % #4
}}

\def\putdtrianglep<#1>(#2,#3)[#4`#5`#6;#7`#8`#9]{{%
\settriparms[#1]%
\xpos=#2 \ypos=#3
\puthmorphism(\xpos,\ypos)[#5`#6`{#9}]{\height}{\arrowtypec}b%
\advance\xpos by \height \advance\ypos by\height
\putmorphism(\xpos,\ypos)(-1,-1)[``{#7}]{\height}{\arrowtypea}l%
\putvmorphism(\xpos,\ypos)[#4``{#8}]{\height}{\arrowtypeb}r%
}}

\def\putdtriangle{\@ifnextchar <{\putdtrianglep}{\putdtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
\def\dtriangle{\@ifnextchar <{\dtrianglep}{\dtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
% #2
\def\dtrianglep<#1>[#2`#3`#4;#5`#6`#7]{{%% % / |
\settriparms[#1]% % / |
\width=\height % #5/ |#6
\diagram% % / |
\putdtrianglep<\arrowtypea`\arrowtypeb`% % / |
\arrowtypec;\height>% % v v
(0,0)[#2`#3`#4;#5`#6`{#7}]% % #3----->#4
\enddiagram%% % #7
}}

\def\putbtrianglep<#1>(#2,#3)[#4`#5`#6;#7`#8`#9]{{%
\settriparms[#1]%
\xpos=#2 \ypos=#3
\puthmorphism(\xpos,\ypos)[#5`#6`{#9}]{\height}{\arrowtypec}b%
\advance\ypos by\height
\putmorphism(\xpos,\ypos)(1,-1)[``{#8}]{\height}{\arrowtypeb}r%
\putvmorphism(\xpos,\ypos)[#4``{#7}]{\height}{\arrowtypea}l%
}}

\def\putbtriangle{\@ifnextchar <{\putbtrianglep}{\putbtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
\def\btriangle{\@ifnextchar <{\btrianglep}{\btrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
% #2
\def\btrianglep<#1>[#2`#3`#4;#5`#6`#7]{{%% % | \
\settriparms[#1]% % | \
\width=\height % #5| \#6
\diagram% % | \
\putbtrianglep<\arrowtypea`\arrowtypeb`% % | \
\arrowtypec;\height>% % v v
(0,0)[#2`#3`#4;#5`#6`{#7}]% % #3----->#4
\enddiagram%% % #7
}}

\def\putAtrianglep<#1>(#2,#3)[#4`#5`#6;#7`#8`#9]{{%
\settriparms[#1]%
\xpos=#2 \ypos=#3
{\multiply \height by2
\puthmorphism(\xpos,\ypos)[#5`#6`{#9}]{\height}{\arrowtypec}b}%
\advance\xpos by\height \advance\ypos by\height
\putmorphism(\xpos,\ypos)(-1,-1)[#4``{#7}]{\height}{\arrowtypea}l%
\putmorphism(\xpos,\ypos)(1,-1)[``{#8}]{\height}{\arrowtypeb}r%
}}

\def\putAtriangle{\@ifnextchar <{\putAtrianglep}{\putAtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
\def\Atriangle{\@ifnextchar <{\Atrianglep}{\Atrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
% #2
\def\Atrianglep<#1>[#2`#3`#4;#5`#6`#7]{{%% % / \
\settriparms[#1]% % / \
\width=\height % #5/ \#6
\diagram% % / \
\putAtrianglep<\arrowtypea`\arrowtypeb`% % / \
\arrowtypec;\height>% % v v
(0,0)[#2`#3`#4;#5`#6`{#7}]% % #3------------>#4
\enddiagram%% % #7
}}

\def\putAtrianglepairp<#1>(#2)[#3;#4`#5`#6`#7`#8]{{%
\settripairparms[#1]%
\setpos(#2)%
\settokens`#3`%
\puthmorphism(\xpos,\ypos)[\tokenb`\tokenc`{#7}]{\height}{\arrowtyped}b%
\advance\xpos by\height
\puthmorphism(\xpos,\ypos)[\phantom{\tokenc}`\tokend`{#8}]%
{\height}{\arrowtypee}b%
\advance\ypos by\height
\putmorphism(\xpos,\ypos)(-1,-1)[\tokena``{#4}]{\height}{\arrowtypea}l%
\putvmorphism(\xpos,\ypos)[``{#5}]{\height}{\arrowtypeb}m%
\putmorphism(\xpos,\ypos)(1,-1)[``{#6}]{\height}{\arrowtypec}r%
}}

\def\putAtrianglepair{\@ifnextchar <{\putAtrianglepairp}{\putAtrianglepairp%
<\arrowtypea`\arrowtypeb`\arrowtypec`\arrowtyped`\arrowtypee;\height>}}
\def\Atrianglepair{\@ifnextchar <{\Atrianglepairp}{\Atrianglepairp%
<\arrowtypea`\arrowtypeb`\arrowtypec`\arrowtyped`\arrowtypee;\height>}}

\def\Atrianglepairp<#1>[#2;#3`#4`#5`#6`#7]{{% % #2a
\settripairparms[#1]% % / | \
\settokens`#2`% % / | \
\width=\height % #3/ #4 \#5
\diagram% % / | \
\putAtrianglepairp % / | \
<\arrowtypea`\arrowtypeb`\arrowtypec`% % v v v
\arrowtyped`\arrowtypee;\height>% % #2b---->#2c---->#2d
(0,0)[{#2};#3`#4`#5`#6`{#7}]% % #6 #7
\enddiagram%%
}}

\def\putVtrianglep<#1>(#2,#3)[#4`#5`#6;#7`#8`#9]{{%
\settriparms[#1]%
\xpos=#2 \ypos=#3
\advance\ypos by\height
{\multiply\height by2
\puthmorphism(\xpos,\ypos)[#4`#5`{#7}]{\height}{\arrowtypea}a}%
\putmorphism(\xpos,\ypos)(1,-1)[`#6`{#8}]{\height}{\arrowtypeb}l%
\advance\xpos by\height
\advance\xpos by\height
\putmorphism(\xpos,\ypos)(-1,-1)[``{#9}]{\height}{\arrowtypec}r%
}}

\def\putVtriangle{\@ifnextchar <{\putVtrianglep}{\putVtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
\def\Vtriangle{\@ifnextchar <{\Vtrianglep}{\Vtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
% #5
\def\Vtrianglep<#1>[#2`#3`#4;#5`#6`#7]{{%% % #2------------->#3
\settriparms[#1]% % \ /
\width=\height % \ /
\diagram% % #6\ /#7
\putVtrianglep<\arrowtypea`\arrowtypeb`% % \ /
\arrowtypec;\height>% % \ /
(0,0)[#2`#3`#4;#5`#6`{#7}]% % v v
\enddiagram%% % #4
}}

\def\putVtrianglepairp<#1>(#2)[#3;#4`#5`#6`#7`#8]{{
\settripairparms[#1]%
\setpos(#2)%
\settokens`#3`%
\advance\ypos by\height
\putmorphism(\xpos,\ypos)(1,-1)[`\tokend`{#6}]{\height}{\arrowtypec}l%
\puthmorphism(\xpos,\ypos)[\tokena`\tokenb`{#4}]{\height}{\arrowtypea}a%
\advance\xpos by\height
\puthmorphism(\xpos,\ypos)[\phantom{\tokenb}`\tokenc`{#5}]%
{\height}{\arrowtypeb}a%
\putvmorphism(\xpos,\ypos)[``{#7}]{\height}{\arrowtyped}m%
\advance\xpos by\height
\putmorphism(\xpos,\ypos)(-1,-1)[``{#8}]{\height}{\arrowtypee}r%
}}

\def\putVtrianglepair{\@ifnextchar <{\putVtrianglepairp}{\putVtrianglepairp%
<\arrowtypea`\arrowtypeb`\arrowtypec`\arrowtyped`\arrowtypee;\height>}}
\def\Vtrianglepair{\@ifnextchar <{\Vtrianglepairp}{\Vtrianglepairp%
<\arrowtypea`\arrowtypeb`\arrowtypec`\arrowtyped`\arrowtypee;\height>}}
% #3 #4
\def\Vtrianglepairp<#1>[#2;#3`#4`#5`#6`#7]{{% % #2a---->#2b---->#2c
\settripairparms[#1]% % \ | /
\settokens`#2`% % \ | /
\diagram% % #5\ #6 /#7
\putVtrianglepairp % \ | /
<\arrowtypea`\arrowtypeb`\arrowtypec`% % \ | /
\arrowtyped`\arrowtypee;\height>% % v v v
(0,0)[{#2};#3`#4`#5`#6`{#7}]% % #2d
\enddiagram%%
}}

\def\putCtrianglep<#1>(#2,#3)[#4`#5`#6;#7`#8`#9]{{%
\settriparms[#1]%
\xpos=#2 \ypos=#3
\advance\ypos by\height
\putmorphism(\xpos,\ypos)(1,-1)[``{#9}]{\height}{\arrowtypec}l%
\advance\xpos by\height
\advance\ypos by\height
\putmorphism(\xpos,\ypos)(-1,-1)[#4`#5`{#7}]{\height}{\arrowtypea}l%
{\multiply\height by 2
\putvmorphism(\xpos,\ypos)[`#6`{#8}]{\height}{\arrowtypeb}r}%
}}

\def\putCtriangle{\@ifnextchar <{\putCtrianglep}{\putCtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
\def\Ctriangle{\@ifnextchar <{\Ctrianglep}{\Ctrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
% #2
\def\Ctrianglep<#1>[#2`#3`#4;#5`#6`#7]{{%% % / |
\settriparms[#1]% % #5/ |
\width=\height % / |
\diagram% % v |
\putCtrianglep<\arrowtypea`\arrowtypeb`% % #3 |#6
\arrowtypec;\height>% % \ |
(0,0)[#2`#3`#4;#5`#6`{#7}]% % #7\ |
\enddiagram%% % \ |
}} % v v
% #4
\def\putDtrianglep<#1>(#2,#3)[#4`#5`#6;#7`#8`#9]{{%
\settriparms[#1]%
\xpos=#2 \ypos=#3
\advance\xpos by\height \advance\ypos by\height
\putmorphism(\xpos,\ypos)(-1,-1)[``{#9}]{\height}{\arrowtypec}r%
\advance\xpos by-\height \advance\ypos by\height
\putmorphism(\xpos,\ypos)(1,-1)[`#5`{#8}]{\height}{\arrowtypeb}r%
{\multiply\height by 2
\putvmorphism(\xpos,\ypos)[#4`#6`{#7}]{\height}{\arrowtypea}l}%
}}

\def\putDtriangle{\@ifnextchar <{\putDtrianglep}{\putDtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
\def\Dtriangle{\@ifnextchar <{\Dtrianglep}{\Dtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
% #2
\def\Dtrianglep<#1>[#2`#3`#4;#5`#6`#7]{{%% % | \
\settriparms[#1]% % | \#6
\width=\height % | \
\diagram% % | v
\putDtrianglep<\arrowtypea`\arrowtypeb`% % #5| #3
\arrowtypec;\height>% % | /
(0,0)[#2`#3`#4;#5`#6`{#7}]% % | /#7
\enddiagram%% % | /
}} % v v
% #4
\def\setrecparms[#1`#2]{\width=#1 \height=#2}%
% #4
% #3b<-------#3a x #3b
% ^ | |
% / | |
% #5/ | |
% / | |
% / | |
% / | |
% #3c |#6 |#3a x #5
% \ | |
% \ | |
% #8\ | |
% \ | |
% \ | |
% v v v
% #3d<-------#3a x #3d
% #8

\def\recursep<#1`#2>[#3;#4`#5`#6`#7`#8]{{\m@th
\width=#1 \height=#2
\settokens`#3`
\settowidth{\tempdimen}{$\tokena$}
\ifdim\tempdimen=0pt
\savebox{\tempboxa}{\hbox{$\tokenb$}}%
\savebox{\tempboxb}{\hbox{$\tokend$}}%
\savebox{\tempboxc}{\hbox{$#6$}}%
\else
\savebox{\tempboxa}{\hbox{$\hbox{$\tokena$}\times\hbox{$\tokenb$}$}}%
\savebox{\tempboxb}{\hbox{$\hbox{$\tokena$}\times\hbox{$\tokend$}$}}%
\savebox{\tempboxc}{\hbox{$\hbox{$\tokena$}\times\hbox{$#6$}$}}%
\fi
\ypos=\height
\divide\ypos by 2
\xpos=\ypos
\advance\xpos by \width
\bfig
\putCtrianglep<-1`1`1;\ypos>(0,0)[`\tokenc`;#5`#6`{#7}]%
\puthmorphism(\ypos,0)[\tokend`\usebox{\tempboxb}`{#8}]{\width}{-1}b%
\puthmorphism(\ypos,\height)[\tokenb`\usebox{\tempboxa}`{#4}]{\width}{-1}a%
\advance\ypos by \width
\putvmorphism(\ypos,\height)[``\usebox{\tempboxc}]{\height}1r%
\efig
}}

\def\recurse{\@ifnextchar <{\recursep}{\recursep<\width`\height>}}

\def\puttwohmorphisms(#1,#2)[#3`#4;#5`#6]#7#8#9{{%
% 1 and 2 are position, 3 and 4 are the nodes, 5 and 6 the labels,
% 7 the distance between node centers and 8 & 9 are the arrow types.
% #5
% #3 ===========> #4
% #6
%
\puthmorphism(#1,#2)[#3`#4`]{#7}0a
\ypos=#2
\advance\ypos by 20
\puthmorphism(#1,\ypos)[\phantom{#3}`\phantom{#4}`#5]{#7}{#8}a
\advance\ypos by -40
\puthmorphism(#1,\ypos)[\phantom{#3}`\phantom{#4}`#6]{#7}{#9}b
}}

\def\puttwovmorphisms(#1,#2)[#3`#4;#5`#6]#7#8#9{{%
% 1 and 2 are position, 3 and 4 are the nodes, 5 and 6 the labels,
% 7 the distance between node centers and 8 & 9 are the arrow types.
%
% #3
% ||
% ||
% #5 || #6
% ||
% ||
% vv
% #4
%
\putvmorphism(#1,#2)[#3`#4`]{#7}0a
\xpos=#1
\advance\xpos by -20
\putvmorphism(\xpos,#2)[\phantom{#3}`\phantom{#4}`#5]{#7}{#8}l
\advance\xpos by 40
\putvmorphism(\xpos,#2)[\phantom{#3}`\phantom{#4}`#6]{#7}{#9}r
}}

\def\puthcoequalizer(#1)[#2`#3`#4;#5`#6`#7]#8#9{{%
% #1 is (\xpos,\ypos), the next 6 are the nodes and arrow labels
% #8 is the distance between each pair of nodes and #9 is the pos of #7
% either a (above) or b (below)
% #5 #7
% #2 ===========> #3 --------> #4
% #6
%
\setpos(#1)%
\puttwohmorphisms(\xpos,\ypos)[#2`#3;#5`#6]{#8}11%
\advance\xpos by #8
\puthmorphism(\xpos,\ypos)[\phantom{#3}`#4`#7]{#8}1{#9}
}}

\def\putvcoequalizer(#1)[#2`#3`#4;#5`#6`#7]#8#9{{%
% #1 is (\xpos,\ypos), the next 6 are the nodes and arrow labels
% #8 is the distance between each pair of nodes and #9 is the pos of #7
% either l (left) or r (right)
%
% #2
% | |
% | |
% #5 | | #6
% | |
% | |
% v v
% #3
% |
% |
% #7 |
% |
% v
% #4
%
\setpos(#1)%
\puttwovmorphisms(\xpos,\ypos)[#2`#3;#5`#6]{#8}11%
\advance\ypos by -#8
\putvmorphism(\xpos,\ypos)[\phantom{#3}`#4`#7]{#8}1{#9}
}}

\def\putthreehmorphisms(#1)[#2`#3;#4`#5`#6]#7(#8)#9{{%
% Use: \putthreehmorphisms(xpos,ypos)[lnode`rnode;toplabel`midlabel%
% botlabel]{distance}(toparrowtype,midarrowtype,botarrowtype){position}
\setpos(#1) \settypes(#8)
\if a#9 %
\vertsize{\tempcounta}{#5}%
\vertsize{\tempcountb}{#6}%
\ifnum \tempcounta<\tempcountb \tempcounta=\tempcountb \fi
\else
\vertsize{\tempcounta}{#4}%
\vertsize{\tempcountb}{#5}%
\ifnum \tempcounta<\tempcountb \tempcounta=\tempcountb \fi
\fi
\advance \tempcounta by 60
\puthmorphism(\xpos,\ypos)[#2`#3`#5]{#7}{\arrowtypeb}{#9}
\advance\ypos by \tempcounta
\puthmorphism(\xpos,\ypos)[\phantom{#2}`\phantom{#3}`#4]{#7}{\arrowtypea}{#9}
\advance\ypos by -\tempcounta \advance\ypos by -\tempcounta
\puthmorphism(\xpos,\ypos)[\phantom{#2}`\phantom{#3}`#6]{#7}{\arrowtypec}{#9}
}}

\def\setarrowtoks[#1`#2`#3`#4`#5`#6]{%
\def\toka{#1}
\def\tokb{#2}
\def\tokc{#3}
\def\tokd{#4}
\def\toke{#5}
\def\tokf{#6}
}
\def\hex{\@ifnextchar <{\hexp}{\hexp<1000`400>}}
\def\hexp<#1`#2>[#3`#4`#5`#6`#7`#8;#9]{%
\setarrowtoks[#9]
\yext=#2 \advance \yext by #2
\xext=#1 \advance\xext by \yext
\bfig
\putCtriangle<-1`0`1;#2>(0,0)[`#5`;\tokb``\tokd]
\xext=#1 \yext=#2 \advance \yext by #2
\putsquare<1`0`0`1;\xext`\yext>(#2,0)[#3`#4`#7`#8;\toka```\tokf]
\advance \xext by #2
\putDtriangle<0`1`-1;#2>(\xext,0)[`#6`;`\tokc`\toke]
\efig
}
%\def\doublecomplex[#1`#2`#3`#4`#5`#6`#7`#8`#9]{%
%\bfig
%\putsquare<0`0`1`1;500`500>(0,1700)[`\vdots`\cdots`{#1};```]
%\puthmorphism(500,1700)[\ph{#1}`\cdots`]{500}1a
%\puthmorphism(1000,1700)[\ph{\cdots}`\ph{#2}`]{500}1a
%\putsquare<0`1`1`1;700`500>(1500,1700)[\vdots`\vdots`{#2}`{#3};```]
%\puthmorphism(2200,1700)[\ph{#3}`0`]{500}1a
%\putvmorphism(500,1700)[`\vdots`]{400}1a \putvmorphism(500,1300)[``]{400}1a
%\putvmorphism(1500,1700)[`\vdots`]{400}1a \putvmorphism(1500,1300)[``]{400}1a
%\putvmorphism(2200,1700)[`\vdots`]{400}1a \putvmorphism(2200,1300)[``]{400}1a
%\putsquare<1`0`1`1;500`500>(0,400)[\cdots`{#4}`\cdots`{#7};```]
%\puthmorphism(500,900)[\ph{#1}`\cdots`]{500}1a
%\puthmorphism(1000,900)[\ph{\cdots}`\ph{#2}`]{500}1a
%\puthmorphism(500,400)[\ph{#1}`\cdots`]{500}1a
%\puthmorphism(1000,400)[\ph{\cdots}`\ph{#2}`]{500}1a
%\putsquare<1`1`1`1;700`500>(1500,400)[{#5}`{#6}`{#8}`{#9};```]
%\puthmorphism(2200,900)[\ph{#6}`0`]{500}1a
%\puthmorphism(2200,400)[\ph{#9}`0`]{500}1a
%\putvmorphism(500,400)[`0`]{400}1a
%\putvmorphism(1500,400)[`0`]{400}1a
%\putvmorphism(2200,400)[`0`]{400}1a
%\efig
%}
%
%\def\doublecocomplex[#1`#2`#3`#4`#5`#6`#7`#8`#9]{%
%\bfig
%\putsquare<0`0`-1`-1;500`500>(0,1700)[`\vdots`\cdots`{#1};```]
%\puthmorphism(500,1700)[\ph{#1}`\cdots`]{500}{-1}a
%\puthmorphism(1000,1700)[\ph{\cdots}`\ph{#2}`]{500}{-1}a
%\putsquare<0`-1`-1`-1;500`500>(1500,1700)[\vdots`\vdots`{#2}`{#3};```]
%\puthmorphism(2000,1700)[\ph{#3}`0`]{500}{-1}a
%\putvmorphism(500,1700)[`\vdots`]{400}{-1}a \putvmorphism(500,1300)[``]{400}{-1}a
%\putvmorphism(1500,1700)[`\vdots`]{400}{-1}a \putvmorphism(1500,1300)[``]{400}{-1}a
%\putvmorphism(2000,1700)[`\vdots`]{400}{-1}a \putvmorphism(2000,1300)[``]{400}{-1}a
%\putsquare<-1`0`-1`-1;500`500>(0,400)[\cdots`{#4}`\cdots`{#7};```]
%\puthmorphism(500,900)[\ph{#1}`\cdots`]{500}{-1}a
%\puthmorphism(1000,900)[\ph{\cdots}`\ph{#2}`]{500}{-1}a
%\puthmorphism(500,400)[\ph{#1}`\cdots`]{500}{-1}a
%\puthmorphism(1000,400)[\ph{\cdots}`\ph{#2}`]{500}{-1}a
%\putsquare<-1`-1`-1`-1;500`500>(1500,400)[{#5}`{#6}`{#8}`{#9};```]
%\puthmorphism(2000,900)[\ph{#6}`0`]{500}{-1}a
%\puthmorphism(2000,400)[\ph{#9}`0`]{500}{-1}a
%\putvmorphism(500,400)[`0`]{400}{-1}a
%\putvmorphism(1500,400)[`0`]{400}{-1}a
%\putvmorphism(2000,400)[`0`]{400}{-1}a
%\efig
%}
\makeatother