Definition 22.3.1 (Compact object). Let \(C\) be an \(\infty \)-category with filtered colimits. An object \(X\in C\) is called compact if the functor \(\Hom _C(X,-)\colon C\to \An \) preserves filtered colimits. We write \(C^\omega \subseteq C\) for the full subcategory of compact objects.
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