Kerodon

Corollary 9.1.9.12. Let $\kappa $ be a small cardinal. Then an $\infty $-category $\operatorname{\mathcal{C}}$ admits small $\kappa $-filtered colimits if and only if it admits $\operatorname{N}_{\bullet }(A)$-indexed colimits, for every small $\kappa $-directed partially ordered set $(A, \leq )$. In this case, a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is $\kappa $-finitary if and only if preserves $\operatorname{N}_{\bullet }(A)$-indexed colimits, for every small $\kappa $-directed partially ordered set $(A, \leq )$.