3

I am using tikz and the following code to make a commutative diagram.

 \documentclass{article}
 \usepackage{tikz-cd, mathtools} 
 \usetikzlibrary{calc}
 \usetikzlibrary{arrows}

 \begin{document}

 \begin{equation*}
 \begin{tikzcd}
 V^{1*} \arrow{r}{\Pi_1(T)} \arrow[dashed, swap]{dr}{g} & V^{2} \\
 & U \arrow[dashed, swap]{u}{h} 
 \end{tikzcd} \hspace{10mm} \text{dim}(U) = r
 \end{equation*}

 \end{document}

enter image description here

I am trying to place a circular arrow in the diagram to indicate that it is commutative. Any help would be greatly appreciated!

4

One way to do this is to name the arrow labeled g. Then a phantom arrow from the 1,2-entry to the name can be labeled with a circular arrow. A phantom arrow is used so only the label appears.

enter image description here

\documentclass{article}
\usepackage{tikz-cd,amssymb}

\begin{document}

\[
\begin{tikzcd}
    V^{1*} \arrow{r}{\Pi_1(T)} \arrow[dashed, swap, ""{name=G}]{dr}{g} & V^{2} \\
    & U \arrow[dashed, swap]{u}{h} \arrow[from=1-2, to=G, pos=.4, phantom, "\circlearrowleft"]
\end{tikzcd} \hspace{10mm} \dim(U) = r
\]

\end{document}

I positioned the circle arrow 40% along the phantom arrow, but you can adjust as you like.

The amssymb package is needed for \circlearrowleft. Also, \dim is already defined, so you don't need to use \text.

0

Among the commutative diagrams there is an old package that I like although it is syntactically unclear. I simply wanted to point out how in some cases the code is reduced by using this type of package. Nowadays we use tikz-cd, but it is a pleasure to know that the xy package fits tikz-cd as far as arrowheads are concerned...See the cmtip option.

\documentclass[12pt]{article}
\usepackage[cmtip,all]{xy}
\usepackage{amssymb}
\begin{document}
\[
\xymatrix@R=1.5pc@C=3pc{\ar @{} [dr]^{\circlearrowleft}
V^{1*} \ar@{-->}[dr]_g \ar[r]^{\Pi_1(T)} & V^{2} \ar@{<--}[d]^h \\ 
& U } \hspace{1cm}\dim(U)=r
\]
\[
\xymatrix@R=1.5pc@C=3pc{\ar @{} [dr]^{\circlearrowleft}
V^{1*} \ar@{.>}[dr]_g \ar[r]^{\Pi_1(T)} & V^{2} \ar@{<.}[d]^h \\ 
& U } \hspace{1cm}\dim(U)=r
\]
\end{document}

enter image description here

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