# Category:Definitions/Abelian Categories

This category contains definitions related to Abelian Categories.
Related results can be found in Category:Abelian Categories.

### 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.

## Pages in category "Definitions/Abelian Categories"

The following 2 pages are in this category, out of 2 total.