Remark 6.3.3.7. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories which exhibits $\operatorname{\mathcal{D}}$ as a localization of $\operatorname{\mathcal{C}}$ with respect to some collection $W$ of morphisms of $\operatorname{\mathcal{C}}$. It follows from Proposition 6.3.3.6 that if $F$ admits a right adjoint $G$, then $G$ is automatically fully faithful. We will see later that the essential image of $G$ is the full subcategory of $\operatorname{\mathcal{C}}$ spanned by the $W$-local objects (Corollary 8.4.4.7).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$