Kerodon

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

Corollary 9.2.1.9. Let $\kappa $ be a small regular cardinal. Then an $\infty $-category $\operatorname{\mathcal{C}}$ is cocomplete if and only if it is $\kappa $-cocomplete and admits small $\kappa $-filtered colimits.

Proof. Apply Proposition 9.2.1.7 in the special case where $\lambda = \operatorname{\Omega }$ is a strongly inaccessible cardinal (see Example 9.1.7.11). $\square$