Remark 4.5.1.20. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be an equivalence of $\infty $-categories. Then the induced functor $\mathrm{h} \mathit{F}: \mathrm{h} \mathit{\operatorname{\mathcal{C}}} \rightarrow \mathrm{h} \mathit{\operatorname{\mathcal{D}}}$ is an equivalence of ordinary categories. In particular, a morphism $u$ in the $\infty $-category $\operatorname{\mathcal{C}}$ is an isomorphism if and only if $F(u)$ is an isomorphism in the $\infty $-category $\operatorname{\mathcal{D}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$