nLab Bousfield localization



Bousfield localization is a sophisticated version of the general idea of localization. We can localize a category by formally inverting certain morphisms: for example, when forming the homotopy category of a model category, where we invert morphisms called ‘weak equivalences’. But Bousfield localization is a subtler process. In the case of a model category, Bousfield localization allows us to make more morphisms count as weak equivalences. There is a related notion of Bousfield localization for triangulated categories.

Left Bousfield localization

Left Bousfield localizations model reflective localizations of (∞,1)-categories.

Right Bousfield localization

Right Bousfield localizations model coreflective localizations of (∞,1)-categories.

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