Remark 4.8.2.12. Let $n$ be an integer and let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories which can be realized as the colimit of a filtered diagram $\{ F_{\alpha }: \operatorname{\mathcal{C}}_{\alpha } \rightarrow \operatorname{\mathcal{D}}_{\alpha } \} $ in the category $\operatorname{Fun}( [1], \operatorname{Set_{\Delta }})$. If each $F_{\alpha }$ is an $n$-full functor of $\infty $-categories, then $F$ is an $n$-full functor of $\infty $-categories.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$