Kerodon

Corollary 9.1.2.8. Let $\operatorname{\mathcal{C}}$ be a category. Then the category $\operatorname{\mathcal{C}}$ is filtered (in the sense of Definition 9.1.0.1) if and only if the $\infty $-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ is filtered (in the sense of Definition 9.1.1.1).