Remark 9.1.5.6. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. It follows from the proof of Proposition 9.1.5.5 that $\operatorname{\mathcal{C}}$ is filtered if and only if it is weakly contractible and satisfies the conclusion of Lemma 9.1.5.4.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$