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Universal property of the product in category theory.

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\begin{diagram}
    &              & Y             &               &     \\
    & \ldTo<{f_1}  & \dDashTo>f    & \rdTo>{\;f_2} &     \\
X_1 & \lTo_{\pi_1} & X_1\times X_2 & \rTo_{\pi_2}  & X_2 \\
\end{diagram}

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