User:TakuyaMurata/Bousfield localization

In algebraic topology, Bousfield localization is a technique in stable homotopy theory.

Localization and completion of a spectrum at a prime number p are both examples of Bousfield localization, resulting in a local spectrum. For example, localizing the sphere spectrum S at p, one obtains a local sphere $$S_{(p)}$$.

Category theory
In category theory, a branch of mathematics, a Bousfield localization of a model category replaces the model structure with another module strcture with the same cofibrations but with more weak equivalences.

See this nlab page for more of this.