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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 wikiPageLength "6912".
• Pre-abelian_category wikiPageOutDegree "70".
• Pre-abelian_category wikiPageRevisionID "618227304".
• Pre-abelian_category wikiPageWikiLink Abelian_categories.
• Pre-abelian_category wikiPageWikiLink Abelian_category.
• Pre-abelian_category wikiPageWikiLink Abelian_group.
• Pre-abelian_category wikiPageWikiLink Additive_category.
• Pre-abelian_category wikiPageWikiLink Additive_functor.
• Pre-abelian_category wikiPageWikiLink Biproduct.
• Pre-abelian_category wikiPageWikiLink Category:Additive_categories.
• Pre-abelian_category wikiPageWikiLink Category_theory.
• Pre-abelian_category wikiPageWikiLink Closed_monoidal_category.
• Pre-abelian_category wikiPageWikiLink Closed_set.
• Pre-abelian_category wikiPageWikiLink Closure_(topology).
• Pre-abelian_category wikiPageWikiLink Coequaliser.
• Pre-abelian_category wikiPageWikiLink Coequalizer.
• Pre-abelian_category wikiPageWikiLink Coimage.
• Pre-abelian_category wikiPageWikiLink Cokernel.
• Pre-abelian_category wikiPageWikiLink Cokernel_(category_theory).
• Pre-abelian_category wikiPageWikiLink Colimit.
• Pre-abelian_category wikiPageWikiLink Complete_category.
• Pre-abelian_category wikiPageWikiLink Coproduct.
• Pre-abelian_category wikiPageWikiLink Direct_sum_of_groups.
• Pre-abelian_category wikiPageWikiLink Enriched_category.
• Pre-abelian_category wikiPageWikiLink Epimorphism.
• Pre-abelian_category wikiPageWikiLink Equaliser_(mathematics).
• Pre-abelian_category wikiPageWikiLink Equalizer_(mathematics).
• Pre-abelian_category wikiPageWikiLink Exact_functor.
• Pre-abelian_category wikiPageWikiLink Exact_sequence.
• Pre-abelian_category wikiPageWikiLink Field_(mathematics).
• Pre-abelian_category wikiPageWikiLink Finite_set.
• Pre-abelian_category wikiPageWikiLink Finitely_complete_category.
• Pre-abelian_category wikiPageWikiLink Function_(mathematics).
• Pre-abelian_category wikiPageWikiLink Group_homomorphism.
• Pre-abelian_category wikiPageWikiLink Hausdorff_space.
• Pre-abelian_category wikiPageWikiLink Hom-set.
• Pre-abelian_category wikiPageWikiLink Identity_element.
• Pre-abelian_category wikiPageWikiLink If_and_only_if.
• Pre-abelian_category wikiPageWikiLink Image_(category_theory).
• Pre-abelian_category wikiPageWikiLink Initial_and_terminal_objects.
• Pre-abelian_category wikiPageWikiLink Isomorphic.
• Pre-abelian_category wikiPageWikiLink Isomorphism.
• Pre-abelian_category wikiPageWikiLink Kernel_(algebra).
• Pre-abelian_category wikiPageWikiLink Kernel_(category_theory).
• Pre-abelian_category wikiPageWikiLink Limit_(category_theory).
• Pre-abelian_category wikiPageWikiLink Mathematics.
• Pre-abelian_category wikiPageWikiLink Module_(mathematics).
• Pre-abelian_category wikiPageWikiLink Monoidal_category.
• Pre-abelian_category wikiPageWikiLink Monomorphism.
• Pre-abelian_category wikiPageWikiLink Morphism.
• Pre-abelian_category wikiPageWikiLink Nicolae_Popescu.
• Pre-abelian_category wikiPageWikiLink Normal_monomorphism.
• Pre-abelian_category wikiPageWikiLink Normal_morphism.
• Pre-abelian_category wikiPageWikiLink Preadditive_categories.
• Pre-abelian_category wikiPageWikiLink Preadditive_category.
• Pre-abelian_category wikiPageWikiLink Product_(category_theory).
• Pre-abelian_category wikiPageWikiLink Range_(function).
• Pre-abelian_category wikiPageWikiLink Range_(mathematics).
• Pre-abelian_category wikiPageWikiLink Ring_(mathematics).
• Pre-abelian_category wikiPageWikiLink Set_(mathematics).
• Pre-abelian_category wikiPageWikiLink Topological_group.
• Pre-abelian_category wikiPageWikiLink Universal_quantification.
• Pre-abelian_category wikiPageWikiLink Vector_space.
• Pre-abelian_category wikiPageWikiLink Zero_morphism.
• Pre-abelian_category wikiPageWikiLink Zero_object.
• Pre-abelian_category wikiPageWikiLinkText "Pre-abelian category".
• Pre-abelian_category wikiPageWikiLinkText "pre".
• Pre-abelian_category wikiPageWikiLinkText "pre-abelian category".
• Pre-abelian_category wikiPageWikiLinkText "pre-abelian".
• Pre-abelian_category hasPhotoCollection Pre-abelian_category.
• Pre-abelian_category subject Category:Additive_categories.
• Pre-abelian_category hypernym Category.
• Pre-abelian_category type TelevisionStation.
• 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 "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 wasDerivedFrom Pre-abelian_category?oldid=618227304.
• Pre-abelian_category isPrimaryTopicOf Pre-abelian_category.