Proposition 4.6.1.21. Let $q: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be an inner fibration of $\infty $-categories and let $X$ and $Y$ be objects of $\operatorname{\mathcal{C}}$. Then the induced map $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y) \rightarrow \operatorname{Hom}_{\operatorname{\mathcal{D}}}( q(X), q(Y) )$ is a Kan fibration of simplicial sets.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$