Kerodon

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

Exercise 11.5.0.54 (Symmetry). Let $T \rightarrow S \leftarrow X$ be a diagram of simplicial sets. Show that the homotopy fiber products $T \times _{S}^{h} X$ and $X \times _{S}^{h} T$ have the same weak homotopy type (see Proposition 3.4.1.9 for a related statement).