Definition:Abelian Category

From ProofWiki
Jump to navigation Jump to search


Definition

Definition 1

An abelian category is a pre-abelian category in which:

every monomorphism is a kernel
every epimorphism is a cokernel


Definition 2

An abelian category is a pre-abelian category in which:

every monomorphism is the kernel of its cokernel
every epimorphism is the cokernel of its kernel


Definition 3

An abelian category is a pre-abelian category in which for every morphism $f$, the canonical morphism from its coimage to its image $\map {\operatorname {coim} } f \to \Img f$ is an isomorphism.


Also see

  • Results about abelian categories can be found here.