Remark 9.1.2.4. Let $\operatorname{\mathcal{C}}$ be an $\mathrm{h} \mathit{\operatorname{Kan}}$-enriched category. If $\operatorname{\mathcal{C}}$ is homotopy filtered (in the sense of Definition 9.1.2.1), then it is filtered when regarded as an ordinary category (in the sense of Definition 9.1.0.1). Beware that the converse is false in general (see Warning 9.1.2.7).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$