# Kerodon

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Definition 7.2.7.4. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category. We say that $\operatorname{\mathcal{C}}$ admits small filtered colimits it admits $\operatorname{\mathcal{K}}$-indexed colimits, for every small filtered $\infty$-category $\operatorname{\mathcal{K}}$. We say that a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ preserves small filtered colimits if it preserves $\operatorname{\mathcal{K}}$-indexed colimits, for every small filtered $\infty$-category $\operatorname{\mathcal{K}}$.