Kerodon

Corollary 9.2.3.12. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then $\operatorname{\mathcal{C}}$ admits small filtered colimits if and only if it is sequentially cocomplete and admits small $\aleph _1$-filtered colimits. If these conditions are satisfied, then a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is finitary if and only if it is $\aleph _1$-finitary and preserves sequential colimits.