Kerodon

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

Corollary 9.2.1.10. Let $\lambda $ be a regular cardinal. Then an $\infty $-category $\operatorname{\mathcal{C}}$ is $\lambda $-cocomplete if and only if it is finitely cocomplete and admits $\lambda $-small filtered colimits.

Proof. Apply Proposition 9.2.1.7 in the special case where $\kappa = \aleph _0$ (see Example 9.1.7.10). $\square$