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.