Kerodon

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

Corollary 3.4.1.3. Suppose we are given a commutative diagram of simplicial sets

3.40
\begin{equation} \label{diagram:homotopy-pullback-square5} \begin{gathered} \xymatrix { Y \ar [r] \ar [d]^{g} & X \ar [d]^{f} \\ T \ar [r] & S, } \end{gathered}\end{equation}

where $f$ is a weak homotopy equivalence. Then (3.40) is homotopy Cartesian if and only if $g$ is a weak homotopy equivalence.