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 an...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.展开更多
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）.
文摘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.
