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The diagram of Snake's Lemma in commutative algebra

How can I draw the dashed line crossing from the right-above to the left-below?

cmhughes
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Victor Chen
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  • Welcome to TeX.SX! If it's just the dashed line across the diagonal you have trouble with, it would be helpful if you could post your code for the rest so it's easier to work on adjusting a ready-made example. – Dai Bowen Nov 05 '16 at 14:56
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    I'm sure we've had exactly this question before.... snake diagram or something similar? – cmhughes Nov 05 '16 at 15:08
  • If this is via xy it is a bit hard, but not impossible. If this is via tikz-cd it is almost trivial. But in any case, please provide some code. (my guess is xy given the arrow heads) – daleif Nov 05 '16 at 15:16
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    See if http://tex.stackexchange.com/questions/3892 is useful. (@cmhughes) – Torbjørn T. Nov 05 '16 at 15:20
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    http://tex.stackexchange.com/questions/31687/bending-snakes-with-xy-pic – cmhughes Nov 05 '16 at 15:29

1 Answers1

3

enter image description here

\documentclass[ tikz,
                border=5mm]{standalone}
% partly based on Loop Space answer on question
% \url{http://tex.stackexchange.com/questions/31687/bending-snakes-with-xy-pic}
\usepackage{amsmath}
\usetikzlibrary{arrows.meta, calc, matrix, quotes}

\DeclareMathOperator{\im}{im}

\begin{document}
\begin{tikzpicture}
\matrix (m) [matrix of math nodes,
             nodes in empty cells,
             nodes={minimum height=4ex,text depth=0.5ex},
             column sep={2.5cm,between origins},
             row sep={2cm,between origins}]
{
    &   0           &   0           &   0           &       \\
%2
0   &   \ker\alpha  &   \ker\beta   &   \ker\gamma  &       \\
%3
0   &   \vert M     &   N           &   P           &   0   \\
%4
0   &   M'          &   N'          &   P'          &   0   \\
%5
    & M'/\im\alpha  & N'/\im\beta   & P'/\im\gamma  &   0   \\
%6
    &   0           &   0           &   0           &       \\
};
%%%% Horizontal arrows,
%   2nd row
\draw[dotted,->]    (m-2-1) -- (m-2-2);
\draw[dashed,->]    (m-2-2) -- (m-2-3);
\draw[dashed,->]    (m-2-3) -- (m-2-4);

\draw[dashed, ->] (m-2-4) to[out=0,in=180] (m-5-2);
%   3th row
\draw[dotted,->]    (m-3-1) -- (m-3-2);
\draw[->]           (m-3-2) -- (m-3-3);
\draw[->]           (m-3-3) -- (m-3-4);
\draw[->]           (m-3-4) -- (m-3-5);
%   4th row
\draw[->]           (m-4-1) -- (m-4-2);
\draw[->]           (m-4-2) -- (m-4-3);
\draw[->]           (m-4-3) -- (m-4-4);
\draw[dotted,->]    (m-4-4) -- (m-4-5);
%   5th row
\draw[dashed,->]    (m-5-2) -- (m-5-3);
\draw[dashed,->]    (m-5-3) -- (m-5-4);
\draw[dotted,->]    (m-5-4) -- (m-5-5);
%%%% Vertical arrows
%   2nd column
\foreach \i in {2,3,4}
\foreach \j [count=\jx from 1] in {2,...,6}
{
\draw[->] (m-\jx-\i) -- (m-\j-\i);
}
%   nodes on arrows in 3th row
\path   (m-3-2) to["$\alpha$"] (m-4-2)
        (m-3-3) to["$\beta$" ] (m-4-3)
        (m-3-4) to["$\gamma$"] (m-4-4);   
\end{tikzpicture}
\end{document}
Zarko
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