Cotorsion Pairs in a Recollement of Triangulated Categories

Chen, Jianmin

doi:10.1080/00927872.2012.666598

Cited by 20 publications

(14 citation statements)

References 10 publications

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“…Later, He-Hu-Zhou [18] glued the torsion pairs via the recollements of extriangulated categories. This unifies their results of Chen [9] and Ma-Huang [22] in the framework of extriangulated categories. Recently, some homological aspects of recollements of extriangulated categories were investigated.…”

Section: Introductionsupporting

confidence: 86%

“…By these frameworks, Wang-Wei-Zhang [35] gave a simultaneous generalization of recollements of abelian categories and triangulated categories, which we call the recollement of extriangulated categories. As an application, they glued the cotorsion pairs along recollements of extriangulated categories, which covers the results obtained by Chen in [9]. Later, He-Hu-Zhou [18] glued the torsion pairs via the recollements of extriangulated categories.…”

Section: Introductionmentioning

confidence: 79%

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s-Recollements and its localization

Hu,

Zhou

2021

Preprint

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We introduce a new concept of s-recollements of extriangulated categories, which generalizes recollements of abelian categories, recollements of triangulated categories, as well as recollements of extriangulated categories. Moreover, some basic properties of s-recollements are presented. We also discuss the behavior of the localization theory on the adjoint pair of exact functors. Finally, we provide a method to obtain a recollement of triangulated categories from s-recollements of extriangulated categories via the localization theory.

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Section: Introductionsupporting

confidence: 86%

Section: Introductionmentioning

confidence: 79%

s-Recollements and its localization

Hu,

Zhou

2021

Preprint

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“…Corollary 3.8. [C,Theorem 3.3] Assume that (A, B, C) is a recollement of triangulated categories. Let (T , F) be a torsion pairs in B. Then…”

Section: Proof (1) For Anymentioning

confidence: 99%

Torsion pairs and recollements of extriangulated categories

Zhou

2021

Preprint

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In this article, we prove that if (A, B, C) is a recollement of extriangulated categories, then torsion pairs in A and C can induce torsion pairs in B, and the converse holds under natural assumptions. Besides, we give mild conditions on a cluster tilting subcategory on the middle category of a recollement of extriangulated categories, for the corresponding abelian quotients to form a recollement of abelian categories.

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“…In recollements of abelian categories, the relations with tilting modules and torsion pairs have been studied in [11] and [9], respectively. Chen [5] studied the relationship of cotorsion pairs among three triangulated categories in a recollement of triangulated categories.…”

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confidence: 99%

Recollements of extriangulated categories

2022

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We give a simultaneous generalization of recollements of abelian categories and triangulated categories, which we call recollements of extriangulated categories. For a recollement (A, B, C) of extriangulated categories, we show that cotorsion pairs in A and C induce cotorsion pairs in B under certain conditions. As an application, our main result recovers a result given by Chen for recollements of triangulated categories, and it also shows a new phenomenon when it is applied to abelian categories.

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Cotorsion Pairs in a Recollement of Triangulated Categories

Cited by 20 publications

References 10 publications

s-Recollements and its localization

s-Recollements and its localization

Torsion pairs and recollements of extriangulated categories

Recollements of extriangulated categories

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