Remark 4.8.5.16 (Change of Target). 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. For $n \geq 1$, the functor $F$ is $n$-full if and only if the composite functor $G \circ F$ is $n$-full. If $G$ is an equivalence of $\infty $-categories, then this is also true when $n = 0$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$