Circular arrow in commutative diagram using tikz

Question

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}

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

Answer 1

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.

\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.

Answer 2

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}