Kerodon

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

Corollary 9.2.2.23. Let $\lambda $ be a regular cardinal and let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories, where $\operatorname{\mathcal{C}}$ is $\lambda $-cocomplete. Then $F$ is $\lambda $-cocontinuous if and only if it is finitely cocontinuous and preserves $\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). $\square$