Kerodon

Corollary 9.1.9.23. Let $\kappa $ be a small regular cardinal. Then an $\infty $-category $\operatorname{\mathcal{C}}$ is cocomplete if and only if it is $\kappa $-cocomplete and admits small $\kappa $-filtered colimits. If these conditions are satisfied, a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ preserves small colimits if and only if it preserves both $\kappa $-small colimits and small $\kappa $-filtered colimits.