Example 4.5.4.12. Suppose we are given a pushout diagram of simplicial sets
4.38
\begin{equation} \label{diagram:categorical-pushout-square9} \begin{gathered} \xymatrix@R =50pt@C=50pt{ A \ar [r]^-{f} \ar [d] & A_0 \ar [d] \\ A_1 \ar [r] & A_{01}. } \end{gathered} \end{equation}
If $f$ is a monomorphism, then (4.38) is also a categorical pushout square.