Definition 9.2.2.1. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category which admits small filtered colimits. We say that an object $C \in \operatorname{\mathcal{C}}$ is compact if the corepresentable functor $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(C, \bullet ): \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{S}}$ is finitary: that is, it preserves small filtered colimits.
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