Left Frobenius Pairs,Cotorsion Pairs and Weak Auslander-Buchweitz Contexts in Triangulated Categories  

作　　者：Xin Ma Tiwei Zhao Zhaoyong Huang Nanqing Ding 

机构地区：[1]College of Science,Henan University of Engineering,Zhengzhou 451191,China [2]School of Mathematical Sciences,Qufu Normal University Qufu,Shandong 273165,China [3]Department of Mathematics,Nanjing University,Nanjing 210093,China [4]不详

出　　处：《Algebra Colloquium》2024年第2期285-308,共24页代数集刊（英文版）

基　　金：supported by the NSF of China(12001168,11901341,11971225,12171207);Henan University of Engineering(DKJ2019010);the Key Research Project of Education Department of Henan Province(21A110006);Youth Innovation Team of Universities of Shandong Province(2022KJ314).

摘　　要：Let T be a triangulated category with a proper classξof triangles.We introduce the notions of left Frobenius pairs,left(n-)cotorsion pairs and left(weak)Auslander-Buchweitz contexts with respect toξin T.We show how to construct left cotorsion pais from left n-cotorsion pairs,and establish a one-to-one correspondence between left Frobenius pairs and left(weak)Auslander-Buchweitz contexts.Some applications are given in the Gorenstein homological theory of triangulated categories.

关 键 词：left Frobenius pairs left n-cotorsion pairs left(weak)Auslander-Buchweitz contexts homological dimensions 

分 类 号：O15[理学—数学]