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.
Some significant examples follow.
Read more about Localization Of A Category: Categorical Definition, Serre's C-theory, Module Theory, Derived Categories, Abelian Varieties Up To Isogeny, Set-theoretic Issues
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