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.
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