Remark 4.6.2.5 (Transitivity). Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ and $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ be functors of $\infty $-categories, where $G$ is fully faithful. Then $F$ is fully faithful if and only if $G \circ F$ is fully faithful. In particular, the collection of fully faithful functors is closed under composition.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$