Abelian category

Summary

An abelian category is an additive category in which every morphism has a kernel and a cokernel. In it, monomorphisms and epimorphisms behave as in abelian groups. In it, exact sequences, homology and the standard diagram lemmas make sense. Modules over a ring and sheaves of abelian groups on a space are abelian categories. Abelian categories were introduced by Buchsbaum and by Grothendieck to give a common framework for homological algebra.