\documentclass{jarticle}
\usepackage[dvipdfm]{graphicx}
\usepackage{tikz}
\usepackage{tikz-cd}
\usetikzlibrary{matrix,arrows,decorations.pathmorphing}
\usetikzlibrary{positioning}
\usepackage{amsmath}

\begin{document}

\date{}
\title{{\bf Commutative Diagram Exmamples}}
\author{}

The tikz package
This is a general purpose graphics package. To load it for this document, I used:


There are now three ways to enter commutative diagrams using tikz: with the package tikz-cd, with matrix, and directly with tikz (listed roughly in order of decreasing ease but increasing flexibility).

\begin{tikzcd}
A \arrow{r}{a} \arrow{d}{b}
               &B \arrow{d}{c}\\
C \arrow{r}{d} &D
\end{tikzcd}

\begin{tikzpicture}
\matrix(m)[matrix of math nodes, row sep=2.6em, column sep=2.8em, text height=1.5ex, text depth=0.25ex]
{A & B \\
 C & D \\ };
\path[->,font=\scriptsize,>=angle 90]
(m-1-1) edge node[auto] {$a$} (m-1-2)
        edge node[auto] {$b$} (m-2-1)
(m-1-2) edge node[auto] {$c$} (m-2-2)
(m-2-1) edge node[auto] {$d$} (m-2-2);
\end{tikzpicture}

\begin{tikzpicture}[scale=1.5]
\node (A) at (0,1) {$A$};
\node (B) at (1,1) {$B$};
\node (C) at (0,0) {$C$};
\node (D) at (1,0) {$D$};
\path[->,font=\scriptsize,>=angle 90]
(A) edge node[above]{$a$} (B)
(A) edge node[right]{$b$} (C)
(B) edge node[right]{$c$} (D)
(C) edge node[above]{$d$} (D);
\end{tikzpicture}


This is part of: Guide to Commutative Diagrams, www.jmilne.org/not/CDGuide.html Last revised October 30, 2012

\begin{tikzcd}
ABC A \arrow[hook]{r}\arrow[two heads]{rd}
                          &B \arrow[dotted]{d}\arrow[hookleftarrow]{r}
&C \arrow[two heads]{ld}\\ D &D
\end{tikzcd}


\begin{tikzcd}
A \arrow[hook]{r}{u}[swap]{b}
Aub Bub C \arrow[two heads]{rd}{u}[swap]{b}
&B \arrow[dotted]{d}{r}[swap]{l}
   \arrow[hookleftarrow]{r}{u}[swap]{b}
D &C \arrow[two heads]{ld}{b}[swap]{u}\\ &D
\end{tikzcd}

\begin{tikzcd}
                        A\arrow{r}\arrow{d}
                        &B\arrow{r}{\text{very long label}}\arrow{d}
                        &C\arrow{d}\\
DEF D\arrow{r}&E\arrow{r}&F 
\end{tikzcd}

% \begin{tikzcd}[column sep=large]
% A\arrow{r}\arrow{d}


\begin{tikzcd}
A B A\arrow[bend left]{r}\arrow[bend right]{r}&B
\end{tikzcd}

\begin{tikzcd}
&A\arrow{ldd}[swap]{f}\arrow{rd}[description]{c}
  \arrow{rrd}[description]{d}
  \arrow{rrrd}[description]{e}\\
&B\arrow{ld}\arrow{r}&C\arrow{r}&D\arrow{r}&E\\
F
\end{tikzcd}

\begin{tikzcd}
T\arrow[bend left]{drr}{x}
\arrow[bend right]{ddr}[swap]{y}
\arrow[dotted]{dr}[description]{(x,y)} & & \\
& X \times_Z Y \arrow{r}{p} \arrow{d}{q} & X \arrow{d}{f} \\
& Y \arrow{r}{g} & Z
\end{tikzcd}

\begin{tikzpicture}[>=angle 90]
\matrix(a)[matrix of math nodes,
row sep=3em, column sep=2.5em,
text height=1.5ex, text depth=0.25ex]
{A&B&C\\
&D\\};
\path[right hook->](a-1-1) edge (a-1-2);
\path[->>](a-1-1) edge (a-2-2);
\path[dotted,->](a-1-2) edge (a-2-2);
\path[left hook->](a-1-3) edge (a-1-2);
\path[->>](a-1-3) edge (a-2-2);
\end{tikzpicture}



\begin{tikzpicture}
\matrix(m)[matrix of math nodes,
row sep=3em, column sep=2.8em,
text height=1.5ex, text depth=0.25ex]
{A&B\\};
\path[->]
(m-1-1) edge [bend left] (m-1-2)
        edge [bend left=40] (m-1-2)
        edge [bend left=60] (m-1-2)
        edge [bend left=80] (m-1-2)
        edge [bend right] (m-1-2);
\end{tikzpicture}

\[
\begin{tikzpicture}[descr/.style={fill=white}]
\matrix(m)[matrix of math nodes, row sep=3em, column sep=2.8em, text height=1.5ex, text depth=0.25ex]
{&A\\&B&C&D&E\\F\\};
\path[->,font=\scriptsize]
(m-1-2) edge node[above left] {$f$} (m-3-1)
        edge node[descr] {$c$} (m-2-3)
        edge node[descr] {$d$} (m-2-4)
        edge node[descr] {$e$} (m-2-5);
\path[->]
(m-2-2) edge (m-3-1)
        edge (m-2-3);
\path[->]
(m-2-3) edge (m-2-4);
\path[->]
(m-2-4) edge (m-2-5);
\end{tikzpicture}
\]

\[
\begin{tikzpicture}[descr/.style={fill=white}]
\matrix(m)[matrix of math nodes, row sep=3em, column sep=2.8em,
text height=1.5ex, text depth=0.25ex]
{T\\&X\times_Z Y&X\\&Y&Z\\};
7

\path[->,font=\scriptsize]
(m-1-1) edge [bend left=10] node[above] {$x$} (m-2-3)
(m-1-1) edge [bend right=10] node[below] {$y$} (m-3-2);
\path[->,dotted,font=\scriptsize]
(m-1-1) edge node[descr] {$(x,y)$} (m-2-2);
\path[->,font=\scriptsize]
(m-2-2) edge node[below] {$p$} (m-2-3)
(m-2-2) edge node[right] {$q$} (m-3-2);
\path[->,font=\scriptsize]
(m-2-3) edge node[right] {$f$} (m-3-3);
\path[->,font=\scriptsize]
(m-3-2) edge node[above] {$g$} (m-3-3);
\end{tikzpicture}
\]

\begin{tikzpicture}
\node (A) at (-1,0) {$A$};
\node (B) at (1,0) {$B$};
\node at (0,0) {\rotatebox{270}{$\Rightarrow$}};
\path[->,font=\scriptsize,>=angle 90]
 (A) edge [bend left] node[above] {$\alpha$} (B)
     edge [bend right] node[below] {$\beta$} (B);
\end{tikzpicture} 

\begin{tikzpicture}
\node (P0) at (90:2.8cm) {$X\otimes (Y\otimes (Z\otimes T))$};
\node (P1) at (90+72:2.5cm) {$X\otimes ((Y\otimes Z)\otimes T))$} ;
\node (P2) at (90+2*72:2.5cm) {${(X\otimes (Y\otimes Z))}\otimes T$};
\node (P3) at (90+3*72:2.5cm) {$((X\otimes Y){\otimes Z)\otimes T}$};
\node (P4) at (90+4*72:2.5cm) {$(X\otimes Y)\otimes (Z\otimes T)$};
\draw
(P0) edge[->,>=angle 90] node[left] {$1\otimes\phi$} (P1)
(P1) edge[->,>=angle 90] node[left] {$\phi$} (P2)
(P2) edge[->,>=angle 90] node[above] {$\phi\otimes 1$} (P3)
(P4) edge[->,>=angle 90] node[right] {$\phi$} (P3)
(P0) edge[->,>=angle 90] node[right] {$\phi$} (P4);
\end{tikzpicture}


\begin{tikzpicture}
\node (a) at (0,0) {$Y\times_X Y$};
\node (b) at (2,0) {$Y$};
\node (c) at (3.5,0) {$X$};
\path[->,font=\scriptsize,>=angle 90]
([yshift= 2pt]a.east) edge node[above] {$p_1$} ([yshift= 2pt]b.west)
([yshift= -2pt]a.east) edge node[below] {$p_2$} ([yshift= -2pt]b.west)
(b) edge (c);
\end{tikzpicture}

\begin{tikzpicture}[descr/.style={fill=white},text height=1.5ex, text depth=0.25ex]
\node (a) at (0,0) {$\mathsf{S}(Z)$};
\node (b) at (2.5,0) {$\mathsf{S}(X)$};
\node (c) at (5,0) {$\mathsf{S}(U).$};
\path[->,font=\scriptsize,>=angle 90]
([yshift= 9pt]b.west) edge node[above] {$i^{\ast}$} ([yshift= 9pt]a.east)
(a.east) edge node[descr] {$i_{\ast}$} (b.west)
([yshift= -9pt]b.west) edge node[below] {$i^!$} ([yshift= -9pt]a.east)
([yshift= 9pt]c.west) edge node[above] {$j_!$} ([yshift= 9pt]b.east)
(b.east) edge node[descr] {$j^{\ast}$} (c.west)
([yshift= -9pt]c.west) edge node[below] {$j_*$} ([yshift= -9pt]b.east);
\end{tikzpicture}


\begin{tikzpicture}[>=angle 90,scale=2.2,text height=1.5ex, text depth=0.25ex]
%%First place the nodes
\node (k-1) at (0,3) {$0$};
\node (k0) [right=of k-1] {$Ker f$};
\node (k1) [right=of k0] {$Ker a$};
\node (k2) [right=of k1] {$Ker b$};
\node (k3) [right=of k2] {$Ker c$};
\node (a1) [below=of k1] {$A$};
\node (a2) [below=of k2] {$B$};
\node (a3) [below=of k3] {$C$};
\node (a4) [right=of a3] {$0$};
\node (b1) [below=of a1] {$A’$};
\node (b0) [left=of b1] {$0$};
\node (b2) [below=of a2] {$B’$};
\node (b3) [below=of a3] {$C’$};
\node (c1) [below=of b1] {$Coker a$};
\node (c2) [below=of b2] {$Coker b$};
\node (c3) [below=of b3] {$Coker c$};
\node (c4) [right=of c3] {$Coker g’$};
\node (c5) [right=of c4] {$0$};
%%Draw the red arrows
\draw[->,red,font=\scriptsize]
(k-1) edge (k0)
(k0)  edge (k1)
(k1)  edge (k2)
(k2)  edge (k3)
(c1)  edge (c2)
(c2)  edge (c3)
(c3)  edge (c4)
(c4)  edge (c5);
%%Draw the curvy red arrow
\draw[->,red]
(k3) edge[out=0,in=180,red] node[pos=0.55,yshift=5pt] {$d$} (c1);
%%Draw the black arrows
\draw[->]
(k1) edge (a1)
(k2) edge (a2)
(k3) edge (a3)
(b1) edge (c1)
(b2) edge (c2)
(b3) edge (c3);
%%Draw the thick blue arrows
\draw[->,font=\scriptsize,blue,thick]
(a1) edge node[auto] {$f$} (a2)
(a2) edge node[auto] {$g$} (a3)
(a3) edge (a4)
(a1) edge node[auto] {$a$} (b1)
(a2) edge node[auto] {$b$} (b2)
(a3) edge node[auto] {$c$} (b3)
(b0) edge (b1)
(b1) edge node[below] {$f’$} (b2)
(b2) edge node[below] {$g’$} (b3);
\end{tikzpicture}


\end{document}