Kerodon

Remark 4.8.5.11. 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 a categorically $n$-connective functor of $\infty $-categories, then $F$ is a categorically $n$-connective functor of $\infty $-categories. See Remark 4.8.2.12.