Localization of extriangulated categories

Nakaoka, Hiroyuki; Ogawa, Yasuaki; Sakai, Arashi

doi:10.1016/j.jalgebra.2022.08.008

Cited by 10 publications

(2 citation statements)

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“…Definition 2.4. [NOS22] Let K be an extriangulated category. We say that a subcategory T ⊂ K is thick, if it is closed under direct summands and if for every conflation X Y ։ Z if two of the terms lie in K, then the third does as well.…”

Section: Cotorsion Pairs and τ -Tilting Theorymentioning

confidence: 99%

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On thick subcategories of the category of projective presentations

Garcı́a¹

2023

Preprint

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We study thick subcategories of the category of 2-term complexes of projective modules over an associative algebra. We show that those thick subcategories that have enough injectives are in explicit bijection with 2-term silting complexes and complete cotorsion pairs. We also provide a bijection with left finite wide subcategories of the module category and prove that all these maps are compatible with previously known correspondences. We discuss possible applications to stability conditions.

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Section: Cotorsion Pairs and τ -Tilting Theorymentioning

confidence: 99%

“…The notion of thick subcategory of an extriangulated category was first introduced in [NOS22] in order to generalize the notion of localization of both exact and triangulated categories. In this paper, we complete the "mirror" version of Theorem A in K [−1,0] (proj Λ) using thick subcategories.…”

Section: Introductionmentioning

confidence: 99%