Editing Localization of a category (section)

In [[mathematics]], '''localization of a category''' consists of adding to a [[Category (mathematics)|category]] inverse [[morphism]]s for some collection of morphisms, constraining them to become [[isomorphism]]s. 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{{what|date=March 2019}}. '''Calculus of fractions''' is another name for working in a localized category.