Remark 4.8.5.3. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories. Then $F$ is fully faithful (in the sense of Definition 4.6.2.1) if and only if it is both full and faithful (in the sense of Definitions 4.8.5.1 and 4.8.5.2).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$