Categories and Weak Equivalences of Graded Algebras  

作　　者：Alexey Gordienko Ofir Schnabel James Zhang 

机构地区：[1]Department of Higher Mathematics,Moscow State Technical University of Civil Aviation Kronshtadtsky Boulevard,d.20,125993 Moscow,Russia [2]Department of Mathematics,ORT Braude College,2161002 Karmicl,Israel [3]不详

出　　处：《Algebra Colloquium》2019年第4期643-664,共22页代数集刊（英文版）

基　　金：supported by Fonds Wetenschappelijk Onderzoek—Vlaanderen post doctoral fellowship(Belgium);supported by the Israel Science Foundation(grant No.1516/16).

摘　　要：In the study of the structure of graded algebras(such as graded ideals,graded subspaces,and radicals)or graded polynomial identities,the grading group can be replaced by any other group that realizes the same grading.Here we come to the notion of weak equivalence of gradings:two gradings are weakly equivalent if there exists an isomorphism between the graded algebras that maps each graded component onto a graded component.Each group grading on an algebra can be weakly equivalent to G-gradings for many different groups G;however,it turns out that there is one distinguished group among them,called the universal group of the grading.In this paper we study categories and functors related to the notion of weak equivalence of gradings.In particular,we introduce an oplax 2-functor that assigns to each grading its support,and show that the universal grading group functor has neither left nor right adjoint.

关 键 词：ALGEBRA GRADING adjoint functor oplax 2-functor (co)limit 

分 类 号：O15[理学—数学]