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Commutative diagram defining a universal morphism from X to U.

See also: Image:UniversalProperty-04.png

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TeX source

\begin{diagram}
X & \rTo^{\varphi} & U(A)            & & A            \\
  & \rdTo_f     & \dDashTo>{U(g)} & & \dDashTo>{g} \\
  &             & U(Y)            & & Y            \\
\end{diagram}