Triangulated Structures Induced by Triangle Functors  

作　　者：Zhibing ZHAO Xianneng DU Yanhong BAO 

机构地区：[1]School of Mathematical Sciences, Anhui University

出　　处：《Chinese Annals of Mathematics,Series B》2019年第1期55-64,共10页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11401001,11571329);the Project of Introducing Academic Leader of Anhui University(No.01001770);the Research Project of Anhui Province(No.KJ2015A101)

摘　　要：Given a triangle functor F : A → B, the authors introduce the half image hIm F,which is an additive category closely related to F. If F is full or faithful, then hIm F admits a natural triangulated structure. However, in general, one can not expect that hIm F has a natural triangulated structure. The aim of this paper is to prove that hIm F admits a natural triangulated structure if and only if F satisfies the condition(SM). If this is the case, hIm F is triangle-equivalent to the Verdier quotient A/Ker F.Given a triangle functor F : A → B, the authors introduce the half image hIm F,which is an additive category closely related to F. If F is full or faithful, then hIm F admits a natural triangulated structure. However, in general, one can not expect that hIm F has a natural triangulated structure. The aim of this paper is to prove that hIm F admits a natural triangulated structure if and only if F satisfies the condition(SM). If this is the case, hIm F is triangle-equivalent to the Verdier quotient A/Ker F.

关 键 词：Triangulated CATEGORY TRIANGLE FUNCTOR HALF image Verdier QUOTIENT 

分 类 号：O1[理学—数学]