In mathematics, localization of a category consists of adding to a category inverse morphisms for some collection of morphisms, constraining them to become isomorphisms. This is formally similar to the process of localization of a ring; it in general makes objects isomorphic that were not so before. In homotopy theory, for example, there are many examples of mappings that are invertible up to homotopy; and so large classes of homotopy equivalent spaces[clarification needed]. Calculus of fractions is another name for working in a localized category.
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In mathematics, localizationofacategory consists of adding to acategory inverse morphisms for some collection of morphisms, constraining them to become...
Look up localization, L10n, or localize in Wiktionary, the free dictionary. Localization or localisation may refer to: Localizationof function, locating...
internationalization and localization (American) or internationalisation and localisation (British), often abbreviated i18n and l10n respectively, are means of adapting...
(mathematics) Local analysis LocalizationofacategoryLocalizationofa module Localizationofa ring Bousfield localization Adams, Frank (1978), Infinite...
simplicial categoryAcategory enriched over simplicial sets. Simplicial localization Simplicial localization is a method oflocalizingacategory. simplicial...
quotient ring modulo a two-sided ideal. The localizationofacategory introduces new morphisms to turn several of the original category's morphisms into isomorphisms...
In category theory, a branch of mathematics, the simplicial localizationofacategory C with respect to a class W of morphisms of C is a simplicial category...
dramatically increases the range of weather conditions in which a safe landing can be made. Other versions of the system, or "categories", have further reduced...
Video game localization (or computer game localisation), is the process of preparing a video game for a market outside of where it was originally published...
denotes the localizationofacategory that inverts every morphism, and C o r e ( C ) {\displaystyle \mathrm {Core} (C)} denotes the subcategory of all isomorphisms...
In category theory, a branch of mathematics, a (left) Bousfield localizationofa model category replaces the model structure with another model structure...
data categories") which are important for internationalization and localization. It also defines implementation of these concepts through a set of elements...
Bousfield localization. For example, the categoryof simplicial sheaves can be obtained as a Bousfield localizationof the model categoryof simplicial...
many categories in mathematics, the categoryof rings is large, meaning that the class of all rings is proper. The category Ring is a concrete category meaning...
sheaves of sets on a topological space (or more generally: on a site). Topoi behave much like the categoryof sets and possess a notion oflocalization; they...
In mathematics, Serre and localizing subcategories form important classes of subcategories of an abelian category. Localizing subcategories are certain...
Simultaneous localization and mapping (SLAM) is the computational problem of constructing or updating a map of an unknown environment while simultaneously...
alocalizing subcategory S ofa compactly generated triangulated category D is generated by a set of objects, then there is a Bousfield localization functor...
In mathematics, the homotopy category is acategory built from the categoryof topological spaces which in a sense identifies two spaces that have the...
prototypical example of an abelian category is the categoryof abelian groups, Ab. Abelian categories are very stable categories; for example they are...
to be equivalent to the localizationofacategory C [ Σ − 1 ] {\displaystyle C[\Sigma ^{-1}]} . The categoryof components ofa PV program P is then defined...
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