Corollary 9.1.8.8. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $\kappa $ be a regular cardinal. Then $\operatorname{\mathcal{C}}$ is $\kappa $-filtered if and only if there exists a $\kappa $-directed partially ordered set $(A, \leq )$ and a right cofinal functor $\operatorname{N}_{\bullet }(A) \rightarrow \operatorname{\mathcal{C}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$