Editing Localization of a category (section)

=== Quotients of abelian categories ===
Given an [[abelian category]] ''A'' and a [[Serre subcategory]] ''B,'' one can define the [[Quotient of an abelian category|quotient category]] ''A/B,'' which is an abelian category equipped with an [[exact functor]] from ''A'' to ''A/B'' that is [[Essentially surjective functor|essentially surjective]] and has kernel ''B.'' This quotient category can be constructed as a localization of ''A'' by the class of morphisms whose kernel and cokernel are both in ''B.''