Corollary 4.4.5.7. Let $q: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be an isofibration of $\infty $-categories. For every simplicial set $B$, the induced map $\operatorname{Fun}(B, \operatorname{\mathcal{C}})^{\simeq } \rightarrow \operatorname{Fun}(B, \operatorname{\mathcal{D}})^{\simeq }$ is a Kan fibration of Kan complexes.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$