Kerodon

Corollary 9.2.2.22. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories, where $\operatorname{\mathcal{C}}$ is cocomplete, and let $\kappa $ be a small regular cardinal. Then $F$ is cocontinuous if and only if it is $\kappa $-cocontinuous and $\kappa $-finitary.