Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
4.32
\begin{equation} \begin{gathered}\label{equation:categorical-pushout-to-categorical-pullback25} \xymatrix@R =50pt@C=50pt{ \operatorname{Fun}( A, \operatorname{Fun}(X, \operatorname{\mathcal{C}}))^{\simeq } & \operatorname{Fun}(A_0, \operatorname{Fun}(X, \operatorname{\mathcal{C}}) )^{\simeq } \ar [l] \\ \operatorname{Fun}(A_1,\operatorname{Fun}( X, \operatorname{\mathcal{C}}))^{\simeq } \ar [u] & \operatorname{Fun}(A_{01}, \operatorname{Fun}(X, \operatorname{\mathcal{C}}))^{\simeq } \ar [u] \ar [l] } \end{gathered} \end{equation}