Example 4.5.5.8. Let $q: X \rightarrow S$ be a Kan fibration of simplicial sets. Then $q$ is an isofibration. To prove this, we note that if a monomorphism of simplicial sets $i: A \hookrightarrow B$ is a categorical equivalence, then it is a weak homotopy equivalence (Remark 4.5.3.4) and therefore anodyne (Corollary 3.3.7.7), so that $q$ has the right lifting property with respect to $i$ (Remark 3.1.2.7).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$