Kerodon

Corollary 9.1.9.13. An $\infty $-category $\operatorname{\mathcal{C}}$ admits small filtered colimits if and only if it admits $\operatorname{N}_{\bullet }(A)$-indexed colimits, for every small directed partially ordered set $(A, \leq )$. In this case, a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is finitary if and only if it preserves $\operatorname{N}_{\bullet }(A)$-indexed colimits, for every small directed partially ordered set $(A, \leq )$.