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\documentclass{article}
\usepackage{xy}
\xyoption{all}
\begin{document}
\pagestyle{empty}
\[
\xymatrix{
& Y \ar[ld]_{f_1} \ar@{-->}[d]^f \ar[rd]^{f_2} & \\
X_1 & X_1 \times X_2 \ar[l]^{\pi_1} \ar[r]_{\pi_2} & X_2 \\
}
\]
\end{document}

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• File:CategoricalProduct-03.png licensed with PD-self
  • 2005-09-24T04:36:00Z Fropuff 213x124 (3355 Bytes) Universal property of the product in category theory.

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