Quotient of an abelian category (original) (raw)

In mathematics, the quotient (also called Serre quotient or Gabriel quotient) of an abelian category by a Serre subcategory is the abelian category which, intuitively, is obtained from by ignoring (i.e. treating as zero) all objects from . There is a canonical exact functor whose kernel is , and is in a certain sense the most general abelian category with this property.