Kerodon

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

Remark 4.1.1.9. Let $f: X \rightarrow S$ be a map of simplicial sets. Suppose that, for every simplex $\sigma : \Delta ^ n \rightarrow S$, the projection map $\Delta ^ n \times _{S} X \rightarrow \Delta ^ n$ is a left fibration (right fibration). Then $f$ is a left fibration (right fibration).