Kerodon

Corollary 9.5.5.14. Let $\kappa $ be a small regular cardinal, let $\operatorname{\mathcal{C}}$ be an $\infty $-category which is cocomplete and $\kappa $-compactly generated (for example, an $\infty $-category which is $\kappa $-presentable), and let $\operatorname{\mathcal{D}}$ be an $\infty $-category which admits small $\kappa $-filtered colimits. Then a functor of $\infty $-categories $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is cocontinuous if and only if it is $\kappa $-finitary and the restriction $F|_{ \operatorname{\mathcal{C}}_{< \kappa } }: \operatorname{\mathcal{C}}_{<\kappa } \rightarrow \operatorname{\mathcal{D}}$ is $\kappa $-cocontinuous.