# Kerodon

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

Corollary 7.2.5.8. Let $\operatorname{\mathcal{C}}$ be a category. Then the category $\operatorname{\mathcal{C}}$ is filtered (in the sense of Definition 7.2.4.1) if and only if the $\infty$-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ is filtered (in the sense of Definition 7.2.4.3).