关于三角商范畴的一个注记  

A NOTE ON TRIANGULATED QUOTIENT CATEGORIES

作　　者：何婧 He Jing(College of Science,Hunan University of Technology and Business,Changsha 410205)

机构地区：[1]湖南工商大学理学院,长沙410205

出　　处：《南京大学学报（数学半年刊）》2022年第2期166-172,共7页Journal of Nanjing University(Mathematical Biquarterly)

摘　　要：设T是带有Serre函子的三角范畴,D?Z是T的两个子范畴且满足Z是扩张封闭τ-稳定的,χ是T中的函子有限子范畴.如果Z中任意的D-monic有锥和D-epic的有余锥,则预三角范畴Z/[D]是一个三角范畴当且仅当(Z,Z)是Dmutation对当且仅当τD=D.作为应用,我们一般化了J?rgensen的结果.Let T be a triangulated category with a Serre functor,and D Z are two subcategories of T such that Z is extension closed T-stable.Let X be a functorially finite subcategory of T.If any D-monic has cone in Z and any D-epic has cocone in Z,then the pre-triangulated category Z/[D]is a triangulated category if and only if(Z,Z)is a D-mutation pair if and only if tD=D.As an application,this generalizes a result of Jorgensen.

关 键 词：三角范畴 Serre函子 扩张封闭子范畴 

分 类 号：O154.1[理学—数学]