Theorem 9.1.5.7. Let $\operatorname{\mathcal{C}}$ be a small $\infty $-category and let $\kappa $ be a small infinite cardinal. Then $\operatorname{\mathcal{C}}$ is $\kappa $-filtered if and only if the colimit functor $\varinjlim : \operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{S}}) \rightarrow \operatorname{\mathcal{S}}$ preserves $\kappa $-small limits.
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