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Commutative diagram defining a universal morphism from U to X.

See also: Image:UniversalProperty-03.png

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TeX source

\begin{diagram}
Y            & & U(Y)            &             &   \\
\dDashTo<{g} & & \dDashTo<{U(g)} & \rdTo^f     &   \\
A            & & U(A)            & \rTo_{\varphi} & X \\
\end{diagram}