% A tin can
% John Baez 
% in LaTeX
% 6/29/10

\documentclass{article}

\usepackage{hyperref}
\usepackage[all]{xy}

\begin{document}


\[
\xymatrix{
U(r)
    \ar@/^1pc/[dd]^{\phi(r)}_{}="0" 
    \ar@/_1pc/[dd]_{\psi(r)}_{}="1" 
    \ar@{=>}"0";"1"_{x(r)}
    \ar[rr]^{U(f)}
&&
U(s)
    \ar@/^1pc/[dd]^{\phi(s)}="0" 
    \ar@{=>}[]+<-2em,-3em>;[ddll]+<4em,3em>_<<<<{\phi(f)}
&&
U(r)
   \ar@/_1pc/[dd]_{\psi(r)}_{}="0" 
   \ar[rr]^{U(f)}
&& 
U(s)
    \ar@/^1pc/[dd]^{\phi(s)}_{}="0" 
    \ar@/_1pc/[dd]_{\psi(s)}_{}="1" 
    \ar@{=>}"0";"1"_{x(s)}
\ar@{=>}[]+<-4em,-3em>;[ddll]+<2em,3em>_<<<<{\psi(f)}
\\
&&& =
\\
V(r)
   \ar[rr]_{V(f)}_{}="1"
&& 
V(s)
&&
V(r) 
   \ar[rr]_{V(f)}_{}="1"
&& 
V(s)
}
\]

\end{document}
