# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Example 4.5.4.12. Suppose we are given a pushout diagram of simplicial sets

4.37
$$\label{diagram:categorical-pushout-square9} \begin{gathered} \xymatrix@R =50pt@C=50pt{ A \ar [r]^-{f} \ar [d] & A_0 \ar [d] \\ A_1 \ar [r] & A_{01}. } \end{gathered}$$

If $f$ is a monomorphism, then (4.37) is also a categorical pushout square.