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Background. I recently came across a Youtube video with a bunch of really nicely typeset 'diagram chases' that seem to have been made in TeX (perhaps TikZ?):

I'd like to create something similar for a presentation that I'm working on, but I feel a bit lost when it comes to figuring out a systematic/scalable way to this.

Own attempt. For small diagrams, it's possible to do this in a very ad hoc way, by just playing around with coordinates and the bend right and bend left attributes in TikZ. A quick example of what this might look like:

documentclass{article}



usepackage{tikz}

usetikzlibrary{arrows.meta}



begin{document}



begin{tikzpicture}[scale=1.5, bend left=15, bend right=15]



        node (B) at (0,0) {$B$};

        node (B') at (0,-1) {$B'$};

        node (C) at (1,0) {$C$};

        node (C') at (1,-1) {$C'$};



        draw[->,gray] (B) -- (B');

        draw[->,gray,shorten >= -1pt] (B') -- (C');

        draw[->,gray,shorten >= -1pt] (B) -- (C);

        draw[->,gray] (C) -- (C');



        node (b) at (-0.3,0.2) {footnotesize $b$};

        node (bprime) at (-0.3,-1.2) {footnotesize $b'$};

        node (cbar) at (0.7,0.2) {footnotesize $bar{c}$};

        node (cdiff) at (0.7,-1.3) {footnotesize $c'-c''$};



        path (b) edge [{|[scale=0.7]}-{>[scale=0.7]},bend left] node [left] {} (cbar);

        path (b) edge [{|[scale=0.7]}-{>[scale=0.7]},bend right] node [left] {} (bprime);

        path (bprime) edge [{|[scale=0.7]}-{>[scale=0.7]},bend right] node [left] {} (cdiff);

        path (cbar) edge [{|[scale=0.7]}-{>[scale=0.7]},bend right, shorten >= -2pt, shorten <= -1pt] node [left] {} (cdiff);



end{tikzpicture}



end{document}

I think this gives a decent end result. But for larger diagrams, it would be an absolute nightmare to work with a code that is so messy and so heavily dependent on coordinates and tweaked parameters.

Thus, if anyone has suggestions (big or small) for a more clever way to do this (with or without TikZ) and/or a way to make my own approach a bit cleaner or more systematic somehow, that would be greatly appreciated!

We clearly can't avoid difficulties and complexity when dealing with such a complicated graph when using any kinds of tool, but by using matrices it has saved a lot of work.

documentclass[tikz]{standalone}

usetikzlibrary{matrix,positioning,arrows.meta}

usepackage{mathptmx}

tikzset{toarrow/.style={{|[scale=0.7]}-{>[scale=0.7]}},

    backarrow/.style={{<[scale=0.7]}-{|[scale=0.7]}}}

begin{document}

begin{tikzpicture}

matrix[matrix of math nodes,row sep=2cm,column sep=2cm] (m) {%

A & B & C & D & E\

A' & B' & C' & D' & E'\};

path   (m-1-2) node[above left=1.5ex and 1.5ex] (b) {$b$}

        (m-1-3) node[above left=1.5ex and 1.5ex] (c) {$c$}

        (m-1-4) node[above left=1.5ex and 1.5ex] (d) {$d$}

        (m-1-5) node[above left=1.5ex and 1.5ex] (e) {$e$}   

        (m-2-2) node[below left=1.5ex and 1.5ex] (b2) {$b'$}

        (m-2-3) node[below left=1.5ex and 1.5ex] (c2) {$c'$}

        (m-2-4) node[below left=1.5ex and 1.5ex] (d2) {$d'$}

        (m-2-5) node[below left=1.5ex and 1.5ex] (e2) {$0$}

        (m-2-3) node[above left=1.5ex and 1.5ex] (c3) {$c''$}

        (c) node[above left=1.5ex and -1.5ex] (cp) {$overline{c}+c$}

        (c2) node[below=1.5ex] (cm) {$c'-c''$}

        (d2) node[below=1.5ex] (db) {$0$}

        (e.base east) node[above right=-.3333em and -1ex] {$=0$}

        (c.base west) node[above left=-.3333em and 1.5ex] (co) {$overline{c}$};

% Delete the following part to see what happens

foreach i [count=j from 2] in {1,2,3,4} {

    draw[dotted,->] (m-1-i) -- (m-2-i);

    draw[dotted,->] (m-1-i) -- (m-1-j);

    draw[dotted,->] (m-2-i) -- (m-2-j);

}

draw[dotted,->] (m-1-5) -- (m-2-5);

draw[toarrow] (b) edge[bend right] (b2) edge[bend left] (co);

draw[toarrow] (b2) to[bend right] (cm);

draw[toarrow] (cm) to[bend right] (db);

draw[toarrow] (co) to[bend right] (cm);

draw[toarrow] (cp) to[bend right] (c2);

draw[toarrow] (c) edge[bend right] (c3) edge[bend left] (d);

draw[backarrow] (d2) edge[bend left] (c2) edge[bend right=20] (c3) edge[bend left] (d);

draw[backarrow] (e2) edge[bend left] (d2) edge[bend left] (e);

draw[toarrow] (d) edge[bend left] (e);

end{tikzpicture}

end{document}