How to draw a commutative diagram?

Question

Is it possible to draw a (simple) commutative diagram using MathJax?

Amscd doesn't seem to work here on math.SE.

M(N)WE:

$$ \begin{CD} K(X) @>{ch}>> H(X;\mathbb Q);\\ @VVV @VVV \\ K(Y) @>{ch}>> H(Y;\mathbb Q); \end{CD} $$

Edit: [A.K. May 7, 2013]

As pointed elsewhere by Davide, this can be remedied now that MathJax 2.2 [beta] is deployed, by adding \require{AMScd}. The code

$$\require{AMScd}
\begin{CD}
K(X) @>{ch}>> H(X;\mathbb Q);\\
@VVV @VVV \\
K(Y) @>{ch}>> H(Y;\mathbb Q);
\end{CD}$$

produces the following diagram:

$$\require{AMScd} \begin{CD} K(X) @>{ch}>> H(X;\mathbb Q);\\ @VVV @VVV \\ K(Y) @>{ch}>> H(Y;\mathbb Q); \end{CD}$$

Answer 1

MathJax 2.2 beta was released recently, and it includes support for AMScd. We have Mathjax 2.2 beta deployed, although without AMScd support for now. Hopefully that too would be added soon enough. As Davide Cervone points out, one can manually load AMScd by adding \require{AMScd} after $$ or $ and using the \begin{CD}...\end{CD} environment. One may want to consult the AMScd manual for instruction on how to draw diagrams with this tool.

While AMScd doesn't support diagonal arrows, it will make rectangular diagrams easier to draw.

Answer 2

It is possible to do (somewhat primitive) commutative diagrams using \array:

$$\begin{array}{ccccccccc} 0 & \xrightarrow{i} & A & \xrightarrow{f} & B & \xrightarrow{q} & C & \xrightarrow{d} & 0\\ \downarrow & \searrow & \downarrow & \nearrow & \downarrow & \searrow & \downarrow & \nearrow & \downarrow\\ 0 & \xrightarrow{j} & D & \xrightarrow{g} & E & \xrightarrow{r} & F & \xrightarrow{e} & 0\end{array}$$

\begin{array}{ccccccccc}   
0 & \xrightarrow{i} & A & \xrightarrow{f} & B & \xrightarrow{q} & C & \xrightarrow{d} & 0\\\

\downarrow & \searrow & \downarrow & \nearrow & \downarrow & \searrow & \downarrow & \nearrow & \downarrow\\\  

0 & \xrightarrow{j} & D & \xrightarrow{g} & E & \xrightarrow{r} & F & \xrightarrow{e} & 0  
end{array}  

I'm not sure it's possible to label diagonal arrows using this approach though.

Answer 3

Here is the commutative diagram from Arturo's fix, touched up to use extensible arrows, and with some spacing tightened up a bit.

$$ \newcommand{\ra}[1]{\!\!\!\!\!\!\!\!\!\!\!\!\xrightarrow{\quad#1\quad}\!\!\!\!\!\!\!\!} \newcommand{\da}[1]{\left\downarrow{\scriptstyle#1}\vphantom{\displaystyle\int_0^1}\right.} % \begin{array}{llllllllllll} 0 & \ra{f_1} & A & \ra{f_2} & B & \ra{f_3} & C & \ra{f_4} & D & \ra{f_5} & 0 \\ \da{g_1} & & \da{g_2} & & \da{g_3} & & \da{g_4} & & \da{g_5} & & \da{g_6} \\ 0 & \ra{h_1} & 0 & \ra{h_2} & E & \ra{h_3} & F & \ra{h_4} & 0 & \ra{h_5} & 0 \\ \end{array} $$

The code is valid in both mathjax and latex. In latex, one should include the amsmath package to get extensible arrows, and I would also recommend less negative spacing (or use a better commutative diagram environment).

$$
\newcommand{\ra}[1]{\!\!\!\!\!\!\!\!\!\!\!\!\xrightarrow{\quad#1\quad}\!\!\!\!\!\!\!\!}
\newcommand{\da}[1]{\left\downarrow{\scriptstyle#1}\vphantom{\displaystyle\int_0^1}\right.}
%
\begin{array}{llllllllllll}
0 & \ra{f_1} & A & \ra{f_2} & B & \ra{f_3} & C & \ra{f_4} & D & \ra{f_5} & 0 \\
\da{g_1} & & \da{g_2} & & \da{g_3} & & \da{g_4} & & \da{g_5} & & \da{g_6} \\
0 & \ra{h_1} & 0 & \ra{h_2} & E & \ra{h_3} & F & \ra{h_4} & 0 & \ra{h_5} & 0 \\
\end{array}
$$

Answer 4

I would modify Jack's answer slightly:

\newcommand{\ra}[1]{\kern-1.5ex\xrightarrow{\ \ #1\ \ }\phantom{}\kern-1.5ex}
\newcommand{\ras}[1]{\kern-1.5ex\xrightarrow{\ \ \smash{#1}\ \ }\phantom{}\kern-1.5ex}
\newcommand{\da}[1]{\bigg\downarrow\raise.5ex\rlap{\scriptstyle#1}}
\begin{array}{c}
0 & \ra{f_1} & A & \ra{f_2} & B & \ra{f_3} & C & \ra{f_4} & D & \ra{f_5} & 0 \\
\da{g_1} & & \da{g_2} & & \da{g_3} & & \da{g_4} & & \da{g_5} & & \da{g_6} \\
0 & \ras{h_1} & 0 & \ras{h_2} & E & \ras{h_3} & F & \ras{h_4} & 0 & \ras{h_5} & 0 \\
\end{array}

$$ \newcommand{\ra}[1]{\kern-1.5ex\xrightarrow{\ \ #1\ \ }\phantom{}\kern-1.5ex} \newcommand{\ras}[1]{\kern-1.5ex\xrightarrow{\ \ \smash{#1}\ \ }\phantom{}\kern-1.5ex} \newcommand{\da}[1]{\bigg\downarrow\raise.5ex\rlap{\scriptstyle#1}} \begin{array}{c} 0 & \ra{f_1} & A & \ra{f_2} & B & \ra{f_3} & C & \ra{f_4} & D & \ra{f_5} & 0 \\ \da{g_1} & & \da{g_2} & & \da{g_3} & & \da{g_4} & & \da{g_5} & & \da{g_6} \\ 0 & \ras{h_1} & 0 & \ras{h_2} & E & \ras{h_3} & F & \ras{h_4} & 0 & \ras{h_5} & 0 \\ \end{array} $$

This would also work in true $\rm\LaTeX$ except for one thing: the \rlap{\scriptstyle#1} would need to be \rlap{$\scriptstyle#1$}.

Answer 5

I have used presheaf in the past, it's really easy (if you know xypic) and comfortable to use.

Answer 6

A potential solution to posting a commutative diagram is to include it as an image. This can allow you have diagonal arrows. :) Here's my workflow for creating commutative diagrams in LaTeX using TikZ. A minimal working LaTeX document looks like this:

\documentclass{standalone}
\usepackage{tikz-cd}

\begin{document}
\begin{tikzcd}
    C \arrow[d,hookrightarrow] \arrow[dr,hookrightarrow,bend left=50,dashed] & &
    \\
    Y \arrow[r,hookrightarrow] \arrow[d,twoheadrightarrow] 
        & X \arrow[d,twoheadrightarrow,dashed] 
            \arrow[dr,twoheadrightarrow,bend left=50] &
    \\
    B \arrow[r,hookrightarrow,dashed] & Y' \arrow[r,twoheadrightarrow,dashed] & A
\end{tikzcd}
\end{document}

Then you can compile this document however you do, zoom into your commutative diagram, take a screenshot, and crop the image.

Or you can avoid taking a screenshot and cropping if you have the other appropriate tools. On my Linux OS I can do this at the command line. I've used this technique on my website, where it's better to have the diagrams be PNG images with transparent backgrounds. For the PDF of the diagram named main.pdf, use

pdftoppm -png -r 600 main.pdf > white.png
convert white.png -fuzz 10% -transparent white transparent.png

That 600 corresponds to the resolution of the image white.png.

See also these questions on other Stack Exchange sites.

• Compile a LaTeX document into a PNG image that's as short as possible
• Standalone diagrams with TikZ?

Answer 7

The simplest Solution is this website. After making the diagram, you can press windows + shift + S, to turn on snipping tool to cut out the diagram and post it elsewhere.

I've made your diagram here. Pic:

---

If you want to remove the dotted lines:

Click the button as shown:

You will get a window, copy code from begin tikzcd to end tikzcd:

Go to overleaf and make a new project, import package tikz-cd, and then, copy previously copied code between begin and end doc like so:

Press the recompile button on middle right to get the diagram, you can scroll below it to see the zoom in button to get better resolution after that:

Final result: