Kerodon

Corollary 9.2.2.28. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category which admits small filtered colimits. Then 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 $(A, \leq )$.