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Tilting pairs in extriangulated categories

Part of: Abelian categories Homological algebra

Published online by Cambridge University Press:  26 October 2021

Tiwei Zhao ,
Bin Zhu  and
Xiao Zhuang
Tiwei Zhao
Affiliation:
School of Mathematical Sciences, Qufu Normal University, Qufu273165, P. R. China ([email protected])
Bin Zhu
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing100084, P. R. China ([email protected])
Xiao Zhuang
Affiliation:
Institute of Mathematics and Physics, Beijing Union University, Beijing100101, P. R. China ([email protected])
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Abstract

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.

Keywords

extriangulated categorytilting pairBazzoni characterizationAuslander–Reiten correspondence

MSC classification

Primary: 18G10: Resolutions; derived functors 18E10: Exact categories, abelian categories
Secondary: 18G25: Relative homological algebra, projective classes
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 64 , Issue 4 , November 2021 , pp. 947 - 981
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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