Remark 9.1.5.11. Let $\operatorname{\mathcal{C}}$ be a filtered $\infty $-category. For every set $I$, condition $(\ast _{I})$ of Corollary 9.1.3.12 depends only on the homotopy category $\operatorname {h}\! \mathit{\operatorname{\mathcal{C}}}$. Applying Proposition 9.1.5.10, we deduce that $\operatorname{\mathcal{C}}$ is $\kappa $-filtered if and only the homotopy category $\operatorname {h}\! \mathit{\operatorname{\mathcal{C}}}$ is $\kappa $-filtered.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$