首页|Balanced Pairs on Triangulated Categories

Balanced Pairs on Triangulated Categories

扫码查看
原文链接
  • NETL
  • NSTL
  • 万方数据
  • 维普
Let C be a triangulated category.We first introduce the notion of balanced pairs in C,and then establish the bijective correspondence between balanced pairs and proper classes ξ with enough ξ-projectives and ξ-injectives.Assume that ξ:=ξx=ξy is the proper class induced by a balanced pair(X,y).We prove that(C,Eξ,sξ)is an extriangulated category.Moreover,it is proved that(C,Eξ,sξ)is a triangulated category if and only if X=y=0,and that(C,Eξ,sξ)is an exact category if and only if X=y=C.As an application,we produce a large variety of examples of extriangulated categories which are neither exact nor triangulated.

triangulated categoryproper classbalanced pairextriangulated category

Xianhui Fu、Jiangsheng Hu、Dongdong Zhang、Haiyan Zhu

展开 >

School of Mathematics and Statistics,Northeast Normal University Changchun 130024,China

School of Mathematics,Hangzhou Normal University Hangzhou 311121,China

Department of Mathematics,Zhejiang Normal University Jinhua,Zhejiang 321004,China

College of Science,Zhejiang University of Technology,Hangzhou 310023,China

展开 >

NSF of ChinaNSF of ChinaNSF of ChinaNatural Science Foundation of Jiangsu ProvinceZhejiang Provincial Natural Science Foundation of ChinaNSF of China

12071064YDZJ202101ZYTS16812171206BK20211358LY18A01003212271481

2023

10.1142/S1005386723000329

代数集刊(英文版)

代数集刊(英文版)

CSCD北大核心
ISSN：1005-3867
年,卷(期)：2023.30(3)
  • 14