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- AB5_category abstract "In mathematics, Grothendieck (1957) in his "Tohoku paper" introduced a sequence of axioms of various kinds of categories enriched over the symmetric monoidal category of abelian groups. Abelian categories are sometimes called AB2 categories, according to the axiom (AB2). AB3 categories are abelian categories possessing arbitrary coproducts (hence by existence of quotients in abelian categories also all colimits). AB5 categories are the AB3 categories in which filtered colimits of exact sequences are exact. Grothendieck categories are the AB5 categories with a generator.".
- AB5_category wikiPageExternalLink 1178244839.
- AB5_category wikiPageID "30051646".
- AB5_category wikiPageLength "1171".
- AB5_category wikiPageOutDegree "9".
- AB5_category wikiPageRevisionID "636316021".
- AB5_category wikiPageWikiLink Abelian_category.
- AB5_category wikiPageWikiLink Axiom.
- AB5_category wikiPageWikiLink Category:Category_theory.
- AB5_category wikiPageWikiLink Category:Homological_algebra.
- AB5_category wikiPageWikiLink Generator_(mathematics).
- AB5_category wikiPageWikiLink Grothendieck_category.
- AB5_category wikiPageWikiLink Grothendiecks_Txc3xb4hoku_paper.
- AB5_category wikiPageWikiLink Mathematics.
- AB5_category wikiPageWikiLink Symmetric_monoidal_category.
- AB5_category wikiPageWikiLink Tohoku_paper.
- AB5_category wikiPageWikiLinkText "AB5 category".
- AB5_category hasPhotoCollection AB5_category.
- AB5_category wikiPageUsesTemplate Template:Citation.
- AB5_category wikiPageUsesTemplate Template:Harvs.
- AB5_category wikiPageUsesTemplate Template:Reflist.
- AB5_category subject Category:Category_theory.
- AB5_category subject Category:Homological_algebra.
- AB5_category type Function.
- AB5_category comment "In mathematics, Grothendieck (1957) in his "Tohoku paper" introduced a sequence of axioms of various kinds of categories enriched over the symmetric monoidal category of abelian groups. Abelian categories are sometimes called AB2 categories, according to the axiom (AB2). AB3 categories are abelian categories possessing arbitrary coproducts (hence by existence of quotients in abelian categories also all colimits).".
- AB5_category label "AB5 category".
- AB5_category sameAs m.0g55fwv.
- AB5_category sameAs Q4650007.
- AB5_category sameAs Q4650007.
- AB5_category wasDerivedFrom AB5_category?oldid=636316021.
- AB5_category isPrimaryTopicOf AB5_category.