Lemma 21.8.8. Let \(L\colon E \to C\) be a Bousfield localization, and let \(W := L^{-1}(C^{\simeq })\) be the class of morphisms in \(E\) inverted by \(L\). Then \(L\) exhibits \(C\) as a localization of \(E\) at \(W\). The same conclusion holds if \(L\) is a Bousfield colocalization.
Proof. See Reference ? of [Cisinski et al. (2026)]. □
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