We investigate the behavior of the extension dimension of subcategories of abelian categories under recollements.LetΛ',Λ,Λ"be art in algebras such that(modΛ',mod A,modΛ")is a recollement,and let...We investigate the behavior of the extension dimension of subcategories of abelian categories under recollements.LetΛ',Λ,Λ"be art in algebras such that(modΛ',mod A,modΛ")is a recollement,and let D'and D"be subcategories of modΛand modΛ"respectively.For any n,m≥0,under some conditions,we get dimΩ^(k)(D)≤dimΩ^(n)(D')+dimΩ^(m)(D")+1,where k=max{m,n}and D is the subcategory of modΛglued by D'and D";moreover,we give a sufficient condition such that the converse inequality holds true.As applications,some results for Igusa-Todorov subcategories and syzygy finite sub categories are obtained.展开更多
Let(A,B,C)be a recollement of extriangulated categories.In this paper we introduce the global dimension and extension dimension of extriangulated categories,and give some upper bounds of global dimensions and extensio...Let(A,B,C)be a recollement of extriangulated categories.In this paper we introduce the global dimension and extension dimension of extriangulated categories,and give some upper bounds of global dimensions and extension dimensions of the categories involved in(A,B,C),which give a simultaneous generalization of some results in recollements of abelian categories and triangulated categories.展开更多
基金Supported by NSFC(Grant Nos.11971225,12171207,12001168)Henan University of Engineering(Grant Nos.DKJ2019010,XTYR-2021JZ001)the Key Research Project of Education Department of Henan Province(Grant No.21A110006)。
文摘We investigate the behavior of the extension dimension of subcategories of abelian categories under recollements.LetΛ',Λ,Λ"be art in algebras such that(modΛ',mod A,modΛ")is a recollement,and let D'and D"be subcategories of modΛand modΛ"respectively.For any n,m≥0,under some conditions,we get dimΩ^(k)(D)≤dimΩ^(n)(D')+dimΩ^(m)(D")+1,where k=max{m,n}and D is the subcategory of modΛglued by D'and D";moreover,we give a sufficient condition such that the converse inequality holds true.As applications,some results for Igusa-Todorov subcategories and syzygy finite sub categories are obtained.
基金This work was supported by the NSFC(12001168)Henan University of Engineering(DKJ2019010)+1 种基金the Key Research Project of Education Department of Henan Province(21A110006)the project ZR2021QA001 of Shandong Provincial Natural Science Foundation.
文摘Let(A,B,C)be a recollement of extriangulated categories.In this paper we introduce the global dimension and extension dimension of extriangulated categories,and give some upper bounds of global dimensions and extension dimensions of the categories involved in(A,B,C),which give a simultaneous generalization of some results in recollements of abelian categories and triangulated categories.
