Remark 22.3.8 (Compact presentations). A presentable \(\infty \)-category \(D\) is compactly generated if and only if it admits a presentation \[ D\simeq \PSh (C)^{S\text {-}\mathrm {loc}} \] in which \(C\) is small and \(S\) is a small collection of morphisms between compact objects of \(\PSh (C)\). We will not use this characterization; see [Lurie (2009), Corollary 5.5.7.3 and Proposition 5.5.7.8].
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