# group actions in diagrams

I am currently finishing a math paper where I have several diagrams with group actions and just plain morphisms. I need the proper denotation for group actions (a round arrow).

Currently, the code looks like this:

\begin{align*}
\xymatrix{
G_1 \ar@{^{(}->}[rd] & & G_2 \ar@{^{(}->}[ld] \ar@{^{(}->}[rd] & & G_1 \ar@{^{(}->}[ld] \\
& \ar[ld]_-{a_1} X_1 \ar[rd]_-{b_1} & & \ar[ld]_-{a_2} X_2 \ar[rd]_-{b_2} & \\
A & & B & & A
}
\end{align*}


The groups G_1 and G_2 act on the spaces. But in this diagram the actions look more like inclusions.

Another situation common in my paper:

$\xymatrix{ G_1 \ar@{^{(}->}[r] & \ar[dl]_{a} X \ar[dr]_{b} & \ar@{^{(}->}[l] G_2 \\ A & & B }$


I want to replace these weird looking inclusions by a symbol for group actions, namely the round arrows.

How could I do this specifically in \xymatrix? Is there a way at all? If you can give me some pstricks hack or something which works in any LaTeX distribution that would be my favorite solution (without having to add packages like tikz, as I fear the math journal will not be able to compile the file).

The question looks similar to a commutative diagram compatible with group actions but in my case the diagram is different.

I have added a picture of what I have in mind. Btw, I find the tikz arrows not pretty either...

In case you change your opinion towards TikZ:

% arara: pdflatex

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

\begin{document}
$\begin{tikzcd} G_1 \ar[hook]{rd} & & G_2 \ar[hook]{ld} \ar[hook]{rd} & & G_1 \ar[hook]{ld} \\ & \ar{ld}{a_1} X_1 \ar{rd}{b_1} & & \ar{ld}{a_2} X_2 \ar{rd}{b_2} & \\ A & & B & & A \end{tikzcd}$
$\begin{tikzcd} G_1\arrow[loop left] \arrow{r} & \arrow{dl}{a} X \arrow{dr}{b} & \arrow{l} G_2\arrow[loop right] \\ A & & B \end{tikzcd}$
\end{document}


If those loops are what you want, you may be interested in how to tweak them:

\begin{document}
\begin{tikzcd}
1\arrow[loop] & 2\arrow[loop above] & 3\arrow[loop above, distance=30] & 4\arrow[loop above, out=70, in=110, distance=30] & 5\arrow[loop, distance=14, out=60, in=30]
\end{tikzcd}
\end{document}


Edit: After the inclusion of the image to the OP, I can update to this solution:

% arara: pdflatex

\documentclass{article}
\usepackage{tikz-cd}
%\tikzcdset{%
%   arrow style=tikz,
%   diagrams={>=stealth}
%}
\tikzset{%
symbol/.style={%
,draw=none
,every to/.append style={%
edge node={node [sloped, allow upside down, auto=false]{$#1$}}}
}
}
\usepackage{amssymb} % for the circle arrows. Chose whatever font you like.

\begin{document}
$\begin{tikzcd}[every label/.append style={swap}] G_1 \arrow[symbol=\circlearrowleft]{rd} & & G_2 \ar[symbol=\circlearrowright]{ld} \ar[symbol=\circlearrowleft]{rd} & & G_1 \ar[symbol=\circlearrowright]{ld} \\[-2\jot] & \ar{ld}{a_1} X_1 \ar{rd}{b_1} & & \ar{ld}{a_2} X_2 \ar{rd}{b_2} & \\ A & & B & & A \end{tikzcd}$
\hrulefill
$\begin{tikzcd}[every label/.append style={swap}] G_1 \arrow[symbol=\circlearrowleft]{r} & \arrow{dl}{a} X\arrow[symbol=\circlearrowright]{r} \arrow{dr}{b} & G_2 \\ A & & B \end{tikzcd}$
\end{document}


• In the first diagram, the arrows connecting the top and midlle rows should be changed to "loop-like" arrows like the ones you used for the actions in the second diagram. – Gonzalo Medina Jun 19 '15 at 15:11
• @GonzaloMedina I was not really sure as the post is not so clear. That's why I posted both. If the OP wants the second approach, this would be clearly a duplicate question. I added some more loops so that the OP can choose what ever fits best. – LaRiFaRi Jun 19 '15 at 15:17
• None of these loops are suitable. In code: G\ \rotatebox[origin=c]{-90}{$\circlearrowright$}\ X is what looks proper to me. The correct answer to my question seems to be at the moment: "There is not a satisfactory solution for group actions in diagrams with LaTeX". – santker heboln Jun 19 '15 at 15:24
• @santkerheboln There is always a solution. See my update. – LaRiFaRi Jun 19 '15 at 15:54
• Thanks. It does look proper this time. Strange that this couldn't be accomplished in xymatrix. – santker heboln Jun 19 '15 at 16:02