# Kerodon

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

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

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

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