Corollary 4.8.8.25. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be an inner fibration of $\infty $-categories and let $n$ be an integer. The following conditions are equivalent:
- $(1)$
The comparison map $G: \mathrm{h}_{\mathit{\leq n}}\mathit{(\operatorname{\mathcal{C}}/\operatorname{\mathcal{D}})} \rightarrow \operatorname{\mathcal{D}}$ is an equivalence of $\infty $-categories.
- $(2)$
The functor $F$ is categorically $(n+1)$-connective.