Corollary 6.2.1.15. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories and let $\mathrm{h} \mathit{F}: \mathrm{h} \mathit{\operatorname{\mathcal{C}}} \rightarrow \mathrm{h} \mathit{\operatorname{\mathcal{D}}}$ be the induced functor of homotopy categories. If $F$ admits a right adjoint $G$, then $\mathrm{h} \mathit{F}$ also admits a right adjoint, which can be identified with the functor $\mathrm{h} \mathit{G}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$