Kerodon

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

Remark 1.4.5.2. Suppose we are given a pullback diagram of simplicial sets

\[ \xymatrix@R =40pt@C=40pt{ X'_{\bullet } \ar [d]^{p'} \ar [r] & X_{\bullet } \ar [d]^{p} \\ Y'_{\bullet } \ar [r] & Y_{\bullet }. } \]

If $p$ is a trivial Kan fibration, then so is $p'$ (this follows from Proposition 1.4.4.5, applied to the opposite of the category $\operatorname{Set_{\Delta }}$).