Commutative Diagrams and TikZ

Question

I wish I knew how to draw the this commutative diagram with the TikZ package.

I would also like to know how to put subtitles in the diagram.

Answer 1

Here's a start diagram for you:

• We use a matrix for the positioning of the main nodes
• We draw edges or arrows, respectively, between the nodes, using nodes for labels
• If you would like to have a caption or subtitle, use a figure environment or the caption package

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
\begin{tikzpicture}
  \matrix (m) [matrix of math nodes,row sep=3em,column sep=4em,minimum width=2em] {
     F_t(x) & F(x) \\
     A_t & A \\};
  \path[-stealth]
    (m-1-1) edge node [left] {$\mathcal{B}_X$} (m-2-1)
            edge [double] node [below] {$\mathcal{B}_t$} (m-1-2)
    (m-2-1.east|-m-2-2) edge node [below] {$\mathcal{B}_T$} node [above] {$\exists$} (m-2-2)
    (m-1-2) edge node [right] {$\mathcal{B}_T$} (m-2-2)
            edge [dashed,-] (m-2-1);
\end{tikzpicture}
\end{document}

Scaling is no problem: simply scale the font by \Large, \Huge etc. The complete matrix will scale because the distances have been given in em units, which scale with the font size. Regarding possibly scaling arrow tips, searching the site should give some hits.

Answer 2

Here's another option using the positioning library, which is nice because you specify nodes in terms of relative positions to one another

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{positioning}

% set arrows as stealth fighter jets
\tikzset{>=stealth}

\begin{document}

\begin{center}
\begin{tikzpicture}
    % set up the nodes
    \node (E) at (0,0) {$F_t(x)$};
    \node[right=of E] (F) {$F(x)$};
    \node[below=of F] (A) {$A$};
    \node[below=of E] (Asubt) {$A_t$};
    % draw arrows and text between them
    \draw[->,double] (E)--(F) node [midway,below] {$\mathcal{B}_T$};
    \draw[->] (F)--(A) node [midway,right] {$\mathcal{B}_T$} 
                node [midway,left] {$\exists$};
    \draw[->] (Asubt)--(A) node [midway,below] {$\mathcal{B}_T$} 
                node [midway,above] {$\exists$};
    \draw[->] (E)--(Asubt) node [midway,left] {$\mathcal{B}_X$};
    \draw[dashed] (Asubt)--(F);
\end{tikzpicture}
\end{center}

\end{document}

Answer 3

Always with tkz-graph

Picture

Code

\documentclass{article}
\usepackage{tkz-graph}
\usetikzlibrary{arrows}

\begin{document}
\begin{tikzpicture}

% unit
\SetGraphUnit{3} 

% style for vertex
\GraphInit[vstyle=Empty] 
\tikzset{VertexStyle/.append style = {shape=rectangle,inner sep=0pt}} 

% vertices  
\Vertex[L=$A_t$]{1} 
\EA[unit=3,L=$A$](1){2} 
\NO[unit=2,L=$F_t(x)$](1){4} 
\NO[unit=2,L=$F(x)$](2){3}

%  edges  and labels 
\begin{scope}[every node/.style={midway},>=latex']  
  \draw[->,double] (4)--(3) node [below] {$\mathcal{B}_T$};
  \draw[->]        (3)--(2) node [right] {$\mathcal{B}_T$} 
                            node [left]  {$\exists$};
  \draw[->]        (1)--(2) node [below] {$\mathcal{B}_T$} 
                            node [above] {$\exists$};
  \draw[->]        (4)--(1) node [left]  {$\mathcal{B}_X$};
  \draw[dashed]    (1)--(3); 
\end{scope}
\end{tikzpicture} 
\end{document}

Answer 4

You can have a shorter code using tikz-cd:

\begin{tikzcd}[swap]
    F_t(x) \arrow[Rightarrow]{r}[inner sep = 1ex]{\mathcal{B}_T} 
           \arrow{d}{\mathcal{B}'_X}
  & F(x) \arrow{d}[swap]{\mathcal{B}_X}{\exists} \\  
    A_t \arrow{r}[swap]{\exists}{\mathcal{B}_T} \arrow[dashed,dash]{ur}
  & A
\end{tikzcd}

Answer 5

The following shows a commutative diagram of the homomorphism theorem. There's a subtlety, which is often forgotten, namely that you shouldn't specify row separations in absolute lenghts but in relative lengths that depend on the size of the type: in my case I am using the em. I specify the distance between the columns and rows is specified in multiples of the type size (ems), not in cm or other units that don't depend on the type size. The advantage of this is that the distances also look good when you scale the picture. (I'm not sure if it's easy to scale the arrows....)

\documentclass{article}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}[every node/.style={midway}]
\matrix[column sep={4em,between origins},
        row sep={2em}] at (0,0)
{ \node(R)   {$R$}  ; & \node(S) {$S$}; \\
  \node(R/I) {$R/I$};                   \\};
\draw[<-] (R/I) -- (R) node[anchor=east]  {$\chi$};
\draw[->] (R/I) -- (S) node[anchor=north]  {$\psi$};
\draw[->] (R)   -- (S) node[anchor=south] {$\phi$};
\end{tikzpicture}

\begin{Huge}
\begin{tikzpicture}[every node/.style={midway}]
\matrix[column sep={4em,between origins},
        row sep={2em}] at (0,0)
{ \node(R)   {$R$}  ; & \node(S) {$S$}; \\
  \node(R/I) {$R/I$};                   \\};
\draw[<-] (R/I) -- (R) node[anchor=east]  {$\chi$};
\draw[->] (R/I) -- (S) node[anchor=north]  {$\psi$};
\draw[->] (R)   -- (S) node[anchor=south] {$\phi$};
\end{tikzpicture}
\end{Huge}

\end{document}

This example may also be found in Chapter 5 of LaTeX and Friends.