In mathematics, localization refers to the idea of adjoining formal inverses for some elements in an algebraic structure.
In particular, the structure itself can be a category, in which case localization adjoins formal inverses to a prescribed class of 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 texts (e.g. in Higher Topos Theory) the term “localization” (when applied to categories or (∞,1)-categories) refers specifically to reflective localizations.
quasicategory of fractions, simplicial localization, hammock localization, simplicial homotopy category
Last revised on June 22, 2024 at 12:58:21. See the history of this page for a list of all contributions to it.