Cluster Subalgebras and Cotorsion Pairs in Frobenius Extriangulated Categories

Chang, Wen Sheng; Zhou, Panyue; Zhu, Bin

doi:10.1007/s10468-018-9811-7

Cited by 24 publications

(10 citation statements)

References 30 publications

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“…After that, the study of extriangulated categories has become an active topic, and up to now, many results on exact categories and triangulated categories have gotten realization in the setting of extriangulated categories by many authors, e.g. see [8, 12, 13, 15–17, 21, 22] and other references.…”

Section: Introductionmentioning

confidence: 99%

Tilting pairs in extriangulated categories

Zhao¹,

Zhu²,

Zhuang³

2021

Proceedings of the Edinburgh Mathematical Society

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Extriangulated categories were introduced by Nakaoka and Palu to give a unification of properties in exact categories and extension-closed subcategories of triangulated categories. A notion of tilting pairs in an extriangulated category is introduced in this paper. We give a Bazzoni characterization of tilting pairs in this setting. We also obtain the Auslander–Reiten correspondence of tilting pairs which classifies finite $\mathcal {C}$ -tilting subcategories for a certain self-orthogonal subcategory $\mathcal {C}$ with some assumptions. This generalizes the known results given by Wei and Xi for the categories of finitely generated modules over Artin algebras, thereby providing new insights in exact and triangulated categories.

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Section: Introductionmentioning

confidence: 99%

Tilting pairs in extriangulated categories

Zhao¹,

Zhu²,

Zhuang³

2021

Proceedings of the Edinburgh Mathematical Society

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“…There have been many further researches on extriangulated categories, see [11,20,26,27] etc. Hu, Zhang and Zhou [17] developed the above mentioned homological algebra in extriangulated categories.…”

Section: Chapter 1 Introductionmentioning

confidence: 99%

Gorenstein Objects in Extriangulated Categories

He¹

2020

Preprint

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This thesis mainly studies the relative Gorenstein objects in the extriangulated category C with a proper class ξ and the related properties of these objects.In the first part, we define the notion of the ξ-Gprojective resolution (see Definition 3.17), and study the relation between ξ-projective resolution and ξ-Gprojective resolution for any object A in C (see Theorem 3.18), i.e. A has a C(−, P(ξ))-exact ξ-projective resolution if and only if A has a C(−, P(ξ))-exact ξ-Gprojective resolution.In the second part, we define a particular ξ-Gorenstein projective object in C which called ξ-n-strongly Gprojective object (see Definition 4.1). On this basis, we study the relation between ξ-m-strongly Gprojective object and ξ-n-strongly Gprojective object whenever m = n (see Theorem 4.6), and give some equivalent characterizations of ξ-n-strongly Gprojective objects (see Theorem 4.8).

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“…After that, the study of extriangulated categories has become an active topic, and up to now, many results on exact categories and triangulated categories have gotten realization in the setting of extriangulated categories by many authors, e.g. see [CZZ,INP,LN,NP19,NP20,PPPP,ZTH,ZZ] and other references.…”

Section: Introductionmentioning

confidence: 99%

Tilting pairs in extriangulated categories

Zhao¹,

Zhu²,

Zhuang³

2020

Preprint

Self Cite

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Extriangulated categories were introduced by Nakaoka and Palu to give a unification of properties in exact categories and extension-closed subcategories of triangulated categories. A notion of tilting pairs in an extriangulated category is introduced in this paper. We give a Bazzoni characterization of tilting pairs in this setting. We also obtain Auslander-Reiten correspondence of tilting pairs which classifies finite C-tilting subcategories for a certain self-orthogonal subcategory C with some assumptions. This generalizes the known results given by Wei and Xi for the categories of finitely generated modules over Artin algebras, thereby providing new insights in exact and triangulated categories.

show abstract

Cluster Subalgebras and Cotorsion Pairs in Frobenius Extriangulated Categories

Cited by 24 publications

References 30 publications

Tilting pairs in extriangulated categories

Tilting pairs in extriangulated categories

Gorenstein Objects in Extriangulated Categories

Tilting pairs in extriangulated categories

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