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Proper resolutions and Gorensteinness in extriangulated categories

Frontiers of Mathematics in China 2021年第1期16卷 95-117页

作者： Jiangsheng HU Dondong ZHANG Panyue ZHOU Department of Mathematics Jiangsu University of TechnologyChangzhou 213001China Department of Mathematics Zhejiang Normal UniversityJinhua 321004China College of Mathematics Hunan Institute of Science and TechnologyYueyang 414006China

Let(C,E,s)be an extriangulated category with a proper classξof E-triangles,and W an additive full subcategory of(C,E,s).We provide a method for constructing a proper W(ξ)-resolution(resp.,coproper W(ξ)-coresolution)of one term in an E-triangle inξfrom that of the other two *** using this way,we establish the stability of the Gorenstein category GW(ξ)in extriangulated *** results generalize the work of ***[***,2013,393:142–169]and *** and ***[Rocky Mountain ***.,2017,47:1013–1053],but the proof is not too far from their ***,we give some applications about our main results.

关键词： Proper resolution coproper coresolution extriangulated categories Gorenstein categories

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Recollements arising from cotorsion pairs on extriangulated categories

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Frontiers of Mathematics in China 2021年第4期16卷 937-955页

作者： Yonggang HU Panyue ZHOU Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China College of Mathematics Hunan Institute of Science and TechnologyYueyang 414006China

This paper is devoted to constructing some recollements of additive categories associated to concentric twin cotorsion pairs on an extriangulated *** an application,this result generalizes the work by ***,***,and *** in a triangulated case[*** Appl.,2018,17(5):1-15].Moreover,it highlights new phenomena when it applied to an exact ***,we give some applications of our main *** particular,we obtain Krause's recollement whose proofs are both elementary and very general.

关键词： extriangulated categories recollements cotorsion pairs adjoint pairs

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Indices and c-vectors in extriangulated categories

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Science China Mathematics 2023年第9期66卷 1949-1964页

作者： Li Wang Jiaqun Wei Haicheng Zhang School of Mathematics-Physics and Finace Anhui Polytechnic UniversityWuhu 241000China Institute of Mathematics School of Mathematical SciencesNanjing Normal UniversityNanjing 210023China

Let C be an extriangulated category and T be any n-cluster tilting subcategory of *** consider the index with respect to T and introduce the index Grothendieck group of *** the index,we prove that the index Grothendieck group of T is isomorphic to the Grothendieck group of C,which implies that the index Grothendieck groups of any two n-cluster tilting subcategories are *** particular,we show that the split Grothendieck groups of any two 2-cluster tilting subcategories are *** we develop a general framework for c-vectors of 2-Calabi-Yau extriangulated categories with respect to arbitrary 2-cluster tilting *** show that the c-vectors have the sign-coherence property and provide some formulas for calculating c-vectors.

关键词： extriangulated categories cluster tilting subcategories indices c-vectors

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Abelian Hearts of Twin Cotorsion Pairs on extriangulated categories

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Algebra Colloquium 2023年第3期30卷 449-466页

作者： Qiong Huang Panyue Zhou Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education)School of Mathematics and Statistics Hunan Normal University Changsha 410081China School of Mathematics and Statistics Changsha University of Science and Technology Changsha 410114China

It was shown recently that the heart of a twin cotorsion pair on an extriangulated category is *** this article,we consider a special class of hearts of twin cotorsion pairs induced by d-cluster tilting subcategories in extriangulated *** give a necessary and sufficient condition for such hearts to be *** particular,we can also see that such hearts are *** an application,this generalizes the work by Liu in the exact case,thereby providing new insights into the triangulated case.

关键词： hearts cotorsion pairs extriangulated categories d-cluster tilting subcate-

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