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Tilting pairs in extriangulated categories

Published online by Cambridge University Press:  26 October 2021

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])

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.

Type
Research Article
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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