Definition 22.3.3. An \(\infty \)-category \(C\) is called compactly generated if it admits small colimits, the subcategory \(C^\omega \) is small, and every object of \(C\) is a filtered colimit of compact objects.
If \(C\) is stable, a small collection \(\Gg \) of compact objects is called a collection of compact generators if the smallest localizing subcategory of \(C\) containing \(\Gg \) is \(C\) itself. Here a localizing subcategory is a full stable subcategory closed under small colimits.
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