Cotorsion Pairs in CN（A）  

作　　者：Xiaoyan Yang Tianya Cao 

机构地区：[1]Department of Mathematics, Northwest Normal University Lanzhou 730070, China

出　　处：《Algebra Colloquium》2017年第4期577-602,共26页代数集刊（英文版）

基　　金：This research was partially supported by the National Natural Science Foundation of China （11361051, 11761060）, Program for New Century Excellent Talents in University （NCET-13-0957）, and Improvement of Young Teachers＇ Scientific Research Ability （NWNU-LKQN-16-5）.

摘　　要：Given a cotorsion pair （X, Y） in an abelian category A, we define cotorsion pairs （XN,dgYN） and （dgXN, YN） in the category CN（A） of N-complexes on A. We prove that if the cotorsion pair （X, Y） is complete and hereditary in a bicomplete abelian category, then both of the induced cotorsion pairs are complete, compatible and hereditary. We also create complete cotorsion pairs （dwXN, （dwXN）⊥）, （eXXN, （exXN）⊥） and （⊥（dwYN）, dwYN）, （X（exYN）, exYN） in a termwise manner by starting with a cotorsion pair （X,Y） that is cogenerated by a set. As applications of these results, we obtain more abelian model structures from the cotorsion pairs.Given a cotorsion pair （X, Y） in an abelian category A, we define cotorsion pairs （XN,dgYN） and （dgXN, YN） in the category CN（A） of N-complexes on A. We prove that if the cotorsion pair （X, Y） is complete and hereditary in a bicomplete abelian category, then both of the induced cotorsion pairs are complete, compatible and hereditary. We also create complete cotorsion pairs （dwXN, （dwXN）⊥）, （eXXN, （exXN）⊥） and （⊥（dwYN）, dwYN）, （X（exYN）, exYN） in a termwise manner by starting with a cotorsion pair （X,Y） that is cogenerated by a set. As applications of these results, we obtain more abelian model structures from the cotorsion pairs.

关 键 词：N-complex cotorsion pair model structure Hovey pair 

分 类 号：O1[理学—数学]