\documentclass{book}
\usepackage[all]{xypic}
\begin{document}
\[\xymatrix{
P^{\prime}
\ar@/_/[ddr]_{p_{2}^{\prime}} \ar@/^/[drr]^{p_{1}^{\prime}}\ar@{>}[dr]|-{p}
\\
& P \ar[d]^{p_{2}}\ar[r]_{p_{1}}&X_{1}\ar[d]_{f_{1}}
\\
&X_{2}\ar[r]^{f_{2}}&Y }\]
\end{document}