Kerodon

Variant 9.1.6.10. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $\kappa $ be a small infinite cardinal. Then $\operatorname{\mathcal{C}}$ 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 $(A, \leq )$. Similarly, a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ preserves small $\kappa $-filtered colimits if and only if it preserves $\operatorname{N}_{\bullet }(A)$-indexed colimits, for every small $\kappa $-directed partially ordered set $(A, \leq )$.