Commutative diagrams can become complicated. They can have many columns, many rows, and a lot of arrow and labels. In such cases, for loops and calculation options can be a relief.

Here, we position the elements in a matrix, and use a loop for drawing the arrows.

The code is fully explained in the LaTeX Cookbook, Chapter 10, Advanced Mathematics, Drawing commutative diagrams.

% Commutative diagram % Author: Stefan Kottwitz % https://www.packtpub.com/hardware-and-creative/latex-cookbook \documentclass[border = 10pt]{standalone} \usepackage{tikz} \usetikzlibrary{matrix,calc} \begin{document} \begin{tikzpicture}[-stealth, label/.style = { font=\footnotesize }] \matrix (m) [ matrix of math nodes, row sep = 4em, column sep = 4em ] { A_0 & A_1 & A_2 & A_3 & A_4 \\ B_0 & B_1 & B_2 & B_3 & B_4 \\ }; \foreach \i in {1,...,4} { \path let \n1 = { int(\i+1) } in (m-1-\i) edge node [above, label] {$f_\i$} (m-1-\n1) (m-2-\i) edge node [below, label] {$f^\prime_\i$} (m-2-\n1) (m-1-\i) edge node [left, label] {$g_\i$} (m-2-\i); } \path (m-1-5) edge node [left, label] {$g_5$} (m-2-5); \end{tikzpicture} \end{document}

Open in Overleaf: five-lemma.tex