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localizationofacategory
localization of a category
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LOCALIZATION OF A CATEGORY - In mathematics, localization of a category consists of adding to a category inverse morphisms for some collection of morphisms, constraining them to ...
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| Localization of a category description |
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| 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. Calculus of fractions is another name for working in a localized category. |