Tilting subcategories in extriangulated categories

doi:10.1007/s11464-020-0811-7

Front. Math. China

2020, Vol. 15

Issue (1) : 225-253 https://doi.org/10.1007/s11464-020-0811-7

RESEARCH ARTICLE

Tilting subcategories in extriangulated categories

Bin ZHU(

), Xiao ZHUANG

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

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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

Corresponding Author(s): Bin ZHU

Issue Date: 09 March 2020

Cite this article:

Bin ZHU,Xiao ZHUANG. Tilting subcategories in extriangulated categories[J]. Front. Math. China, 2020, 15(1): 225-253.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0811-7
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I1/225

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