# Category:Abelian Categories

Jump to navigation
Jump to search

This category contains results about Abelian Categories.

Definitions specific to this category can be found in Definitions/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.

*This category currently contains no pages or media.*