Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Example 4.5.3.8. Suppose we are given a pushout diagram of simplicial sets

4.20
\begin{equation} \label{diagram:categorical-pushout-square9} \begin{gathered} \xymatrix@R =50pt@C=50pt{ A \ar [r]^-{f} \ar [d] & B \ar [d] \\ C \ar [r] & D. } \end{gathered} \end{equation}

If $f$ is a monomorphism, then (4.20) is also a homotopy pushout diagram.