Definition 21.8.1. A functor \(L\colon C \to D\) is called a Bousfield localization if it admits a fully faithful right adjoint \(R\colon D \hookrightarrow C\). In this case, we also call \(D\) a reflective subcategory of \(C\).
A Bousfield colocalization is instead a functor \(C \to D\) that admits a fully faithful left adjoint.
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