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.