Corollary 9.3.7.5. Let $\operatorname{\mathcal{C}}$ be an essentially small $\infty $-category and let $\kappa $ be a small regular cardinal. Then $\operatorname{\mathcal{C}}$ is $\kappa $-filtered if and only if the $\infty $-category $\operatorname{Ind}_{\kappa }(\operatorname{\mathcal{C}})$ has a final object.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Proposition 9.3.7.4 in the case where $\lambda = \Omega $ is a strongly inaccessible cardinal. $\square$