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balanced pairs on Triangulated Categories

Algebra Colloquium 2023年第3期30卷 385-394页

作者： Xianhui Fu Jiangsheng Hu Dongdong Zhang Haiyan Zhu School of Mathematics and Statistics Northeast Normal UniversityChangchun 130024China School of Mathematics Hangzhou Normal UniversityHangzhou 311121China Department of Mathematics Zhejiang Normal UniversityJinhuaZhejiang 321004China College of Science Zhejiang University of TechnologyHangzhou 310023China

Let C be a triangulated *** first introduce the notion of balanced pairs in C,and then establish the bijective correspondence between balanced pairs and proper classesξwith enoughξ-projectives andξ-*** thatξ:=ξX=ξ^(Y) is the proper class induced by a balanced pair(X,Y).We prove that(C,Eξ,sξ)is an extriangulated ***,it is proved that(C,Eξ,sξ)is a triangulated category if and only if X=Y=0,and that(C,Eξ,sξ)is an exact category if and only if X=Y=*** an application,we produce a large variety of examples of extriangulated categories which are neither exact nor triangulated.

关键词： triangulated category proper class balanced pair extriangulated category

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On Proper and Exact Relative Homological Dimensions

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Algebra Colloquium 2020年第3期27卷 621-642页

作者： Driss Bennis J.R.Garcia Rozas Lixin Mao Luis Oyonarte CeReMAR Center Faculty of Sciences B.P.1014 Mohammed V University in RabatRabatMorocco Dcpartamento de Matematicas Universidad de AlmeriaAlmena 04071Spain Department of Mathematics and Physics Nanjing Institute of Technology Nanjing 211167China Departamento de Matematicas Universidad de AlmenaAlmena 04071Spain

In Enochs'relative homological dimension theory occur the(co)resolvent and(co)proper dimensions,which are defined by proper and coproper resolutions constructed by precovers and preenvelopes,***,some authors have been interested in relative homological dimensions defined by just exact *** this paper,we contribute to the investigation of these relative homological *** we study the relation between these two kinds of relative homological dimensions and establish some transfer results under adjoint *** relative global dimensions are studied,which lead to nice characterizations of some properties of particular cases of self-orthogonal *** the end of this paper,relative derived functors are studied and generalizations of some known results of balance for relative homology are established.

关键词： self-orthogonal subcategory resolvent dimension exact dimension relative homological dimension relative group(co)homology balanced pair

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