Balanced Pairs on Triangulated Categories

作     者：Xianhui Fu Jiangsheng Hu Dongdong Zhang Haiyan Zhu Xianhui Fu;Jiangsheng Hu;Dongdong Zhang;Haiyan Zhu

作者机构：School of Mathematics and StatisticsNortheast Normal UniversityChangchun 130024China School of MathematicsHangzhou Normal UniversityHangzhou 311121China Department of MathematicsZhejiang Normal UniversityJinhuaZhejiang 321004China College of ScienceZhejiang University of TechnologyHangzhou 310023China 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2023年第30卷第3期

页      面：385-394页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Xianhui Fu was supported by YDZJ202101ZYTS168 and the NSF of China(12071064) Jiangsheng Hu was supported by the NSF of China(12171206) the Natural Science Foundation of Jiangsu Province(BK20211358) Haiyan Zhu was supported by Zhejiang Provincial Natural Science Foundation of China(LY18A010032) the NSF of China(12271481) 

主　　题：triangulated category proper class balanced pair extriangulated category 

摘      要：Let C be a triangulated *** first introduce the notion of balanced pairs in C,and then establish the bijective correspondence between balanced pairs and proper classesξwith enoughξ-projectives andξ-*** thatξ:=ξX=ξ^(Y) is the proper class induced by a balanced pair(X,Y).We prove that(C,Eξ,sξ)is an extriangulated ***,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=*** an application,we produce a large variety of examples of extriangulated categories which are neither exact nor triangulated.