Theorem 9.1.5.1. Let $\operatorname{\mathcal{C}}$ be a small $\infty $-category. Then $\operatorname{\mathcal{C}}$ is filtered if and only if $\operatorname{\mathcal{C}}$-indexed colimits commute with finite limits in the $\infty $-category of spaces $\operatorname{\mathcal{S}}$ (Definition 9.1.4.2).
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