Tilting subcategories in extriangulated categories
Abstract
Extriangulated category was introduced by Nakaoka and Palu to give a unification of properties in exact categories and triangulated categories. A notion of tilting (or cotilting) subcategories in an extriangulated category is defined in this paper. We give a Bazzoni characterization of tilting (or cotilting) subcategories and obtain an Auslander-Reiten correspondence between tilting (cotilting) subcategories and coresolving covariantly (resolving contravariantly, resp.) finite subcatgories which are closed under direct summands and satisfies some cogenerating (generating, resp.) conditons. Applications of the results are given: we show that tilting (cotilting) subcategories defined here unify many previous works about tilting theory in module categories of Artin algebras and abelian categories admitting a cotorsion triples; we also show that the results work for triangulated categories with a proper class of triangles introduced by Beligiannis.
Keywords
Cite
@article{arxiv.1907.00747,
title = {Tilting subcategories in extriangulated categories},
author = {Bin Zhu and Xiao Zhuang},
journal= {arXiv preprint arXiv:1907.00747},
year = {2019}
}
Comments
28 pages, 0 figures. arXiv admin note: text overlap with arXiv:1605.05607, arXiv:1702.00244 by other authors