nLab localization


In mathematics, localization refers to the idea of formally adding inverses to some elements in an algebraic structure.

In particular, the structure itself can be a category, in which case localization adds formal inverses to morphisms. This construction is known as a category of fractions and also ambiguously as a localization of a category. An important special case of this idea is the notion of a reflective localization / left Bousfield localization, in which case the localization functor has a fully faithful right adjoint. In some books (e.g., Higher Topos Theory) the term “localization” (when applied to categories or (∞,1)-categories) refers specifically to reflective localizations.

For categories and (∞,1)-categories




For commutative rings

For noncommutative rings

For modules

For monoids

For categories of spaces

For categories of spectra

Created on December 26, 2023 at 21:57:56. See the history of this page for a list of all contributions to it.