Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Corollary 4.8.5.22. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories. If $F$ is categorically $n$-connective (in the sense of Definition 4.8.5.1), then it is $n$-connective (in the sense of Variant 3.5.1.15).

Proof. Using Corollary 4.8.5.21 (and Remark 4.5.4.4), 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. $\square$