Example: Snake Lemma

Published 2012-11-18 | Author: Andrew Stacey

This example uses the tikz-cd package because of the “asymmetrical rectangle” node style, and it loads the matrix and calc libraries for cleaner code. A special focus is on drawing the arrow for the connecting homomorphism, answering a question of Jamie Weigandt on TeX.SE.

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Snake Lemma

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% The Snake Lemma
% Author: Andrew Stacey
% Source: http://tex.stackexchange.com/questions/3892/
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage{tikz-cd}
\usetikzlibrary{matrix, calc, arrows}

\DeclareMathOperator{\coker}{coker}

\begin{document}
\begin{tikzpicture}[>=triangle 60]
  \matrix[matrix of math nodes,column sep={60pt,between origins},row
    sep={60pt,between origins},nodes={asymmetrical rectangle}] (s)
  {
    &|[name=ka]| \ker f &|[name=kb]| \ker g &|[name=kc]| \ker h \\
    %
    &|[name=A]| A' &|[name=B]| B' &|[name=C]| C' &|[name=01]| 0 \\
    %
    |[name=02]| 0 &|[name=A']| A &|[name=B']| B &|[name=C']| C \\
    %
    &|[name=ca]| \coker f &|[name=cb]| \coker g &|[name=cc]| \coker h \\
  };
  \draw[->] (ka) edge (A)
            (kb) edge (B)
            (kc) edge (C)
            (A) edge (B)
            (B) edge node[auto] {\(p\)} (C)
            (C) edge (01)
            (A) edge node[auto] {\(f\)} (A')
            (B) edge node[auto] {\(g\)} (B')
            (C) edge node[auto] {\(h\)} (C')
            (02) edge (A')
            (A') edge node[auto] {\(i\)} (B')
            (B') edge (C')
            (A') edge (ca)
            (B') edge (cb)
            (C') edge (cc)
  ;
  \draw[->,gray] (ka) edge (kb)
                 (kb) edge (kc)
                 (ca) edge (cb)
                 (cb) edge (cc)
  ;
  \draw[->,gray,rounded corners] (kc) -| node[auto,text=black,pos=.7]
    {\(\partial\)} ($(01.east)+(.5,0)$) |- ($(B)!.35!(B')$) -|
    ($(02.west)+(-.5,0)$) |- (ca);
\end{tikzpicture}
\end{document}

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