# Kerodon

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Variant 7.2.7.6. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty$-categories. The following conditions are equivalent:

$(1)$

The functor $F$ preserves small filtered colimits.

$(2)$

For every small filtered category $\operatorname{\mathcal{K}}$, the functor $F$ preserves $\operatorname{N}_{\bullet }(\operatorname{\mathcal{K}})$-indexed colimits.

$(3)$

For every directed partially ordered set $(A, \leq )$, the functor $F$ preserves $\operatorname{N}_{\bullet }(A)$-indexed colimits.