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