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

被引：3

作者：

Di, Zhenxing ^{[1
]}

Liu, Zhongkui ^{[1
]}

Wang, Junpeng ^{[1
]}

Wei, Jiaqun ^{[1
,2
]}

机构：

[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

来源：

JOURNAL OF ALGEBRA | 2019年 / 525卷

基金：

中国国家自然科学基金;

关键词：

(pre)silting subcategory; Auslander-Reiten correspondence; Bazzoni's characterization; Silting complex; Tilting complex; TILTING MODULES; T-STRUCTURES; OBJECTS;

D O I：

10.1016/j.jalgebra.2019.01.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：42 / 63

页数：22