Triangle commutative diagram with xymatrix

Question

I'm using the xymatrix package (which I think is more friendly than tikz package), and I've been trying to do a simple triangle diagram with a circle arrow in the middle. I mean, I've done this one:

\documentclass{article}
\usepackage[all]{xy}
\begin{document}
$\xymatrix
   { & \mathcal{L} \ar[dl]_{\pi_j} \ar[dr]^{\pi_i} & \\
     G_j \ar[rr]_{\pi_i^j} & & G_i
   }
$
\end{document}

and I want to add a circle arrow in the middle. I've tried to add rows, but the diagonal arrows became crazy, and the result is awful.

Answer 1

Like this?

\documentclass{article}
\usepackage[all]{xy}
\begin{document}
$\xymatrix
   { & \mathcal{L} \ar[dl]_{\pi_j} \ar[dr]^{\pi_i} \ar[d]|-{\circ} & \\
     G_j \ar[rr]_{\pi_i^j} & & G_i
   }
$
\end{document}

Answer 2

Do you know tikz-cd package? It's not so difficult:

\documentclass{article} 
\usepackage{tikz-cd} 
\usepackage{stix}
\begin{document} 
\begin{tikzcd}[column sep=small, row sep=small] 
    & \mathcal{L} \arrow{ddl}[swap]{\pi_{j}} \arrow{ddr}{\pi_{i}} &\\
    & \circlearrowleft &\\[-2ex]
    G_{j} \arrow{rr}[swap]{\pi_{i}^{j}} & & G_{i} \\
\end{tikzcd}
\end{document}

Answer 3

We're all still guessing what you want it to look like, but here's an attempt:

You'd get that with:

\documentclass{article}
\usepackage{amssymb}
\usepackage[cmtip,all]{xy}

\begin{document}

$\xymatrix{
  & \mathcal{L} \ar[dl]_{\pi_j} \ar[dr]^{\pi_i}
  \ar@{}[d]|-{\circlearrowleft} \\
  G_j \ar[rr]_{\pi_i^j}
  && G_i
}
$

\end{document}