Kerodon

Corollary 9.2.3.9. Let $\kappa $ be a regular cardinal. Then an $\infty $-category $\operatorname{\mathcal{C}}$ is $\kappa ^{+}$-cocomplete if and only if it is both $\kappa $-cocomplete and $\kappa $-sequentially cocomplete. If these conditions are satisfied, then a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is $\kappa ^{+}$-cocontinuous if and only if it is $\kappa $-cocontinuous and preserves $\kappa $-sequential colimits.