# Category:Definitions/Abelian Categories

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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 5 pages are in this category, out of 5 total.