\documentclass{article}

\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{xy}
\usepackage{color}

\xyoption{all}

\begin{document}
\pagestyle{empty}
\[
\xymatrix{
& & Y^\prime
	\ar@{-->}[rrdd]^{g}
	\ar[lldddd]
		^(.6125){[1]}
		|\hole
\\ \\
Z^\prime
	\ar@{-->}[rruu]^{f}
	\ar[dd]_{[1]}
& & & &
X^\prime
	\ar[lldddd]
		_(.3725){i}
		|!{[dd];[uull]}\hole
		|!{[ddllll];[dd]}\hole
	\ar[llll]_{j[1]\circ i}^{[1]}
\\ \\
X
	\ar[rrrr]^{v\circ u}
	\ar[rrdd]_{u}
& & & &
Z
	\ar[uu]
	\ar[lluuuu]
		|\hole
\\ \\
& &
Y
	\ar[rruu]_{v}
	\ar[lluuuu]
		_(.6125){j}
		|!{[lluu];[rruu]}\hole
		|!{[uuuuuu];[lluu]}\hole
}
\]
\end{document}