Corollary 4.8.7.17. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories. If $F$ is categorically $n$-connective, then it is $n$-connective.
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Corollary 4.8.7.17. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories. If $F$ is categorically $n$-connective, then it is $n$-connective.
Proof. Using Corollary 4.8.7.16 (and Remark 4.5.3.4), we can reduce to the case where $F$ is bijective on simplices of dimension $\leq n$. In this case, the desired result follows from Corollary 3.5.2.2. $\square$