\documentclass[12pt]{proc}
\usepackage[all]{xy}
\begin{document}

\noindent Let $\mathcal{C}$ be a category and
let
%
\begin{displaymath}
 \xy\xygraph{ []Z ( [u]X :_f ? , [l]Y :^g ? )
  }\endxy
\end{displaymath}
%
be a given diagram of objects and morphisms in
$\mathcal{C}$.  Construct a category
$\mathcal{K}$ as follows: for the objects of
$\mathcal{K}$ take the commutativity squares
$[X,Y,Z;V]$ of the form
%
\begin{displaymath}
 \xy\xygraph{
  []Z ( [u]X :_f ? , [l]Y :^g ? )
  [ul]V ( ? : "X" , ? : "Y" )
 }\endxy
\end{displaymath}
%
and for the set of morphisms from $[X,Y,Z;V]$ to
$[X,Y,Z;U]$ take the morphisms $v:V\to U$ of
$\mathcal{C}$ such that
%
\begin{displaymath}
 \xy\xygraph{
  []Z   ( [u]X :_f ? , [l]Y :^g ? )
  [ul]V ( ? : "X" , ? : "Y" )
  [ul]U ( ? : "X" , ? : "Y" ,
	  ? : "V" )
 }\endxy
\end{displaymath}
%
is commutative.  A terminal object in
$\mathcal{K}$ is called a {\em pullback\/} for
$f,g$.

\end{document}