An Auslander-Buchweitz approximation approach to (pre)silting subcategories in triangulated categories

JOURNAL OF ALGEBRA

卷:525

Article

Di, Zhenxing¹  Liu, Zhongkui¹  Wang, Junpeng¹  Wei, Jiaqun^1,2 

[1] Northwest Normal Univ, Dept Math, Lanzhou 730070, Gansu, Peoples R China

[2] Nanjing Normal Univ, Sch Math Sci, Inst Math, Nanjing 210023, Jiangsu, Peoples R China

关键词: (pre)silting subcategory;    Auslander-Reiten correspondence;    Bazzoni's characterization;    Silting complex;    Tilting complex;   

DOI  :  10.1016/j.jalgebra.2019.01.021

来源: Elsevier

【 摘 要 】

We apply the Auslander-Buchweitz approximation triangles to study (pre)silting subcategories in a triangulated category T. An Auslander-Reiten type correspondence between the class of silting subcategories of T and that of certain covariantly finite subcategories of T is established. We introduce a relation on presilting subcategories of T, which can be used to obtain another silting subcategory from a given one. We also give a Bazzoni's characterization for two presilting subcategories satisfying such a relation. The results can be used to improve the Auslander-Reiten type correspondence and Bazzoni's characterization for small silting complexes established by Wei. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free