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Tilting subcategories in extriangulated categories

  • Bin ZhuEmail author
  • Xiao Zhuang
Research Article
  • 6 Downloads

Abstract

Extriangulated category was introduced by H. Nakaoka and Y. Palu to give a unification of properties in exact categories and triangulated categories. A notion of tilting (resp., cotilting) subcategories in an extriangulated category is defined in this paper. We give a Bazzoni characterization of tilting (resp., cotilting) subcategories and obtain an Auslander-Reiten correspondence between tilting (resp., cotilting) subcategories and coresolving covariantly (resp., resolving contravariantly) finite subcatgories which are closed under direct summands and satisfy some cogenerating (resp., generating) conditions. Applications of the results are given: we show that tilting (resp., cotilting) subcategories defined here unify many previous works about tilting modules (subcategories) in module categories of Artin algebras and in abelian categories admitting a cotorsion triples; we also show that the results work for the triangulated categories with a proper class of triangles introduced by A. Beligiannis.

Keywords

Extriangulated category tilting subcategory Auslander-Reiten correspondence Bazzoni characterization 

MSC

18E30 16G10 16D90 

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Notes

Acknowledgements

The authors would like to thank Dr. Tiwei Zhao for helpful comments on the paper, and they also would like to thank the referees for reading the paper carefully and for many suggestions on mathematical and English expressions. This work was supported by the National Natural Science Foundation of China (Grant No. 11671221).

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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina

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