In category theory, a localization of a category amounts to making some morphisms isomorphisms. An element in a commutative ring "R" may be thought of as an endomorphism of any "R"-module. Thus, categorically, a localization of "R" with respect to a subset "S" of "R" is a functor from the category of "R"-modules to itself that sends elements of "S" viewed as endomorphisms to automorphisms and is universal with respect to this property. (Of course, "R" then maps to <math>R\leftand "R"-modules map to formula_188-modules.)