Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Corollary 9.2.1.16. Let $\kappa $ and $\lambda $ be small regular cardinals satisfying $\kappa \trianglelefteq \lambda $. Then an $\infty $-category $\operatorname{\mathcal{C}}$ admits small $\kappa $-filtered colimits if and only if it admits small $\lambda $-filtered colimits and is $(\kappa ,\lambda )$-cocomplete.

Proof. Apply Proposition 9.2.2.29 in the special case where $\lambda = \operatorname{\Omega }$ is a fixed strongly inaccessible cardinal (see Example 9.1.7.11). $\square$