xy-pic
I'm trying to do the following with xymatrix:
This is a diagram I drew sometime ago… But now I don't have the source and I can't remember how I did it, nor can I find an easy, simple way to do it.
More specifically, what I forgot how to do is the vertical arrow in the middle.
You can put the framed y inside a \xybox and then compose it with the ,x,z into the complete object. Together with height adjustment this will look like
\documentclass{standalone}
\usepackage{amsmath,amssymb}
\usepackage[all]{xy}
\begin{document}
\[\xymatrix{
x & *+[Fo]{z} \ar[l]\ar[d] & z\ar[l] & \cdots\ar[l]\\
z & \xybox{(0,0.5)*+[Fo]{y}},x,z \ar[l]\ar[d] & \cdots \ar[l]\\
& *+[Fo]{y} & \cdots\ar[l]
}\]
\end{document}
Although if you would want the circled y aligned with the other circled characters, you should probably ask another question about that. (I don't know right now how to do it.)
Please note that you shouldn't use the minimal class. Better take standalone for MWEs. See for example Why should the minimal class be avoided? and What is the advantage of using minimal over article when creating a standalone graphic?.
If you are willing to switch to tikz-cd this becomes easy.
% arara: pdflatex
\documentclass{article}
\usepackage{mathtools}
\usepackage{amsfonts}
\DeclareMathOperator\id{id}
\DeclareMathOperator\pr{pr}
\usepackage{tikz-cd}
\begin{document}
\[
\begin{tikzcd}
p^{-1}(U_{\alpha})\ar{rr}{\tau_{\alpha}} && U_{\alpha}\times\mathbb{R}^k\ar{dl}{\pr_1}\\
& U_{\mathrlap\alpha}\ar{ul}{s|_{U_{\alpha}}}\ar[loop above]{}{\id} &
\end{tikzcd}
\]
\end{document}
In order to manipulate the target of the arrow, you may want to play around with the options in the arrow below.
\begin{tikzcd}
p^{-1}(U_{\alpha})\ar{rr}{\tau_{\alpha}} && U_{\alpha}\times\mathbb{R}^k\ar{dl}{\pr_1}\\
& U_{\mathrlap\alpha}\ar{ul}{s|_{U_{\alpha}}}\ar[%
,loop % tells tikz-cd to do a loop
,out=123 % start at angle 123°
,in=57 % stop at angle 57°
,distance=2.5em % biggest distance of arrow to node. You can use pt or cm as well.
]{}{\id} &
\end{tikzcd}
I just checked the syntax for xy and the default result looks quite good, too. Would this be close enough to the right arrow?
% arara: pdflatex
\documentclass{article}
\usepackage{mathtools}
\usepackage{amsfonts}
\DeclareMathOperator\id{id}
\DeclareMathOperator\pr{pr}
\usepackage[all,cmtip]{xy}
\begin{document}
\[
\xymatrix{%
p^{-1}(U_{\alpha})\ar[rr]^-{\tau_{\alpha}} & & U_{\alpha}\times\mathbb{R}^k\ar[dl]^{\pr_1} \\
& U_{\alpha}\ar[ul]^-{s|_{U_{\alpha}}} \ar@(ul,ur)^{\id} % smashing the alpha here would result in touching arrow heads. That's why I didn't do that here
}. % supposing, this dot was set here by purpose...
\]
\end{document}
Best Answer
The 2cell module is what you need: