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bazzoni characterization

Proceedings of the Edinburgh Mathematical Society (1)

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1 results

Tilting pairs in extriangulated categories
Part of
- Abelian categories
- Homological algebra
Tiwei Zhao, Bin Zhu, Xiao Zhuang
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 64 / Issue 4 / November 2021

Published online by Cambridge University Press:

26 October 2021, pp. 947-981
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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.