\documentclass{amsart}
\usepackage{amsmath,amssymb,nopageno}
\usepackage[all]{xy}
\begin{document}
\begin{equation*}
\xymatrix@=5em{
& Y' \ar@{-->}[dr]^g \ar[ddl]^(0.65){[1]} & \\
Z' \ar@{-->}[ur]^f \ar[d]_{[1]} & &
    X' \ar[ll]_{j[1] \circ i}^{[1]}|(0.25)\hole|(0.75)\hole
       \ar[ddl]_(0.4)i^(0.4){[1]}|(0.25)\hole|(0.5)\hole \\
X \ar[rr]^{v \circ u} \ar[dr]_u & &
    Z \ar[u] \ar[uul]\\
& Y \ar[ur]_v \ar[uul]_(0.6)j|(0.5)\hole|(0.75)\hole &
}
\end{equation*}
\end{document}

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