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- Pre-abelian_category abstract "In mathematics, specifically in category theory, a pre-abelian category is an additive category that has all kernels and cokernels.Spelled out in more detail, this means that a category C is pre-abelian if: C is preadditive, that is enriched over the monoidal category of abelian groups; C has all biproducts, which are both finite products and finite coproducts; given any morphism f: A → B in C, the equaliser of f and the zero morphism from A to B exists (this is the kernel), as does the coequaliser (this is the cokernel).Note that the zero morphism in item 3 can be identified as the identity element of the hom-set Hom(A,B), which is an abelian group by item 1; or as the unique morphism A → O → B, where O is a zero object, guaranteed to exist by item 2.".
- Pre-abelian_category wikiPageID "62775".
- Pre-abelian_category wikiPageRevisionID "603903908".
- Pre-abelian_category hasPhotoCollection Pre-abelian_category.
- Pre-abelian_category subject Category:Additive_categories.
- Pre-abelian_category type Abstraction100002137.
- Pre-abelian_category type AdditiveCategories.
- Pre-abelian_category type Class107997703.
- Pre-abelian_category type Collection107951464.
- Pre-abelian_category type Group100031264.
- Pre-abelian_category comment "In mathematics, specifically in category theory, a pre-abelian category is an additive category that has all kernels and cokernels.Spelled out in more detail, this means that a category C is pre-abelian if: C is preadditive, that is enriched over the monoidal category of abelian groups; C has all biproducts, which are both finite products and finite coproducts; given any morphism f: A → B in C, the equaliser of f and the zero morphism from A to B exists (this is the kernel), as does the coequaliser (this is the cokernel).Note that the zero morphism in item 3 can be identified as the identity element of the hom-set Hom(A,B), which is an abelian group by item 1; or as the unique morphism A → O → B, where O is a zero object, guaranteed to exist by item 2.".
- Pre-abelian_category label "Categoria pré-abeliana".
- Pre-abelian_category label "Pre-abelian category".
- Pre-abelian_category sameAs Categoria_pré-abeliana.
- Pre-abelian_category sameAs m.0gyt1.
- Pre-abelian_category sameAs Q7239192.
- Pre-abelian_category sameAs Q7239192.
- Pre-abelian_category sameAs Pre-abelian_category.
- Pre-abelian_category wasDerivedFrom Pre-abelian_category?oldid=603903908.
- Pre-abelian_category isPrimaryTopicOf Pre-abelian_category.