Almost split triangles and morphisms determined by objects in extriangulated categories

JOURNAL OF ALGEBRA

卷:559

Article

Zhao, Tiwei¹  Tan, Lingling¹  Huang, Zhaoyong² 

[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

[2] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

关键词: Extriangulated categories;    Almost split s-triangles;    Right C-determined morphisms;    s-deflations;    s-inflations;   

DOI  :  10.1016/j.jalgebra.2020.04.021

来源: Elsevier

【 摘 要 】

Let (C, E, s) be an Ext-finite, Krull-Schmidt and k-linear extriangulated category with k a commutative artinian ring. We define an additive subcategory C-r (respectively, C-l) of C in terms of the representable functors from the stable category of C modulo s-injectives (respectively, .s-projectives) to k-modules, which consists of all s-projective (respectively, s-injective) objects and objects isomorphic to direct summands of finite direct sums of all third (respectively, first) terms of almost split s-triangles. We investigate the subcategories C-r and C-l in terms of morphisms determined by objects, and then give equivalent characterizations on the existence of almost split s-triangles. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free