Recollements of extriangulated categories

Wang, Li; Wei, Jiaqun; Zhang, Haicheng

doi:10.48550/arxiv.2012.03258

Cited by 4 publications

(12 citation statements)

References 8 publications

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“…Definition 2.4. [WWZ,Definition 2.8] A morphism f in C is called compatible, if "f is both an inflation and a deflation" implies that f is an isomorphism.…”

Section: Preliminariesmentioning

confidence: 99%

“…Definition 2.8. [WWZ,Definition 2.13] Let (A, E A , s A ) and (B, E B , s B ) be extriangulated categories. We say an additive covariant functor F : A → B is an exact functor if the following conditions hold.…”

Section: Preliminariesmentioning

confidence: 99%

“…Lemma 3.3. [WWZ,Proposition 3.4] Let (A, B, C) be a recollement of triangulated categories and X ∈ B. Then the following statements hold.…”

Section: Glued Torsion Pairsmentioning

confidence: 99%

“…[WWZ, Proposition 2.14] Let (A, E A , s A ) and (B, E B , s B ) be extriangulated categories. An additive covariant functor F : A → B is exact if and only if F is both left exact and right exact.Let us recall the concept of a recollement of extriangulated categories from[WWZ].Definition 2.11.…”

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confidence: 99%

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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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“…Definition 2.4. [WWZ,Definition 2.8] A morphism f in C is called compatible, if "f is both an inflation and a deflation" implies that f is an isomorphism.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

“…Lemma 3.3. [WWZ,Proposition 3.4] Let (A, B, C) be a recollement of triangulated categories and X ∈ B. Then the following statements hold.…”

Section: Glued Torsion Pairsmentioning

confidence: 99%

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confidence: 99%

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Torsion pairs and recollements of extriangulated categories

Zhou

2021

Preprint

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“…A fundamental example of a recollement of abelian categories appeared in the construction of perverse sheaves by MacPherson and Vilonen [21]. A recollement of triangulated (or, abelian, extriangulated) categories, see the references [2,21,35], is a diagram of functors between triangulated (or, abelian, extriangulated) categories of the following shape (1.1), which satisfies some assumptions.…”

Section: Introductionmentioning

confidence: 99%

s-Recollements and its localization

Hu,

Zhou

2021

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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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Localization of extriangulated categories

Nakaoka¹,

Ogawa²,

Sakai³

2021

Preprint

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In this article, we show that the localization of an extriangulated category by a multiplicative system satisfying mild assumptions can be equipped with a natural, universal structure of an extriangulated category. This construction unifies the Serre quotient of abelian categories and the Verdier quotient of triangulated categories. Indeed we give such a construction for a bit wider class of morphisms, so that it covers several other localizations appeared in the literature, such as Rump's localization of exact categories by biresolving subcategories, localizations of extriangulated categories by means of Hovey twin cotorsion pairs, and the localization of exact categories by two-sided admissibly percolating subcategories.

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Recollements of extriangulated categories

Cited by 4 publications

References 8 publications

Torsion pairs and recollements of extriangulated categories

Torsion pairs and recollements of extriangulated categories

s-Recollements and its localization

Localization of extriangulated categories

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