半群分次范畴上的模范畴,Galois盖与Smash积

Module Category over Semigroup Graded Category,Galois Covering and Smash Product

设S为有单位元的可消半群.引入半群S对C-M od的作用及半群S分次C-模范畴的概念,证明了当C为B的G a lo is盖时,B-模范畴与C的不动点满子范畴是一致的.对半群S分次B-模范畴,Sm ash积B#S-模范畴与半群S分次B-模范畴是一致的;同时还讨论了半群S分次模的Sm ash积,刻画了Sm ash积函子#与(-)*之间的关系.

Let S be a cancellable semigroup with identity 1. Introduces the definitions of S action on L-Mod and S-graded L-Mod. It proves that in case of a Galois covering of category L to B, the category B- Mod of B-modules coincides with the full subcategory of the fixed modules over the category L, while to the S-graded B-Mod, the category B # S-Mod of B # S-modules coincides with the category of S-graded B- modules. As to the S-graded B-module M, introduces M # S and discusses the relationship between the functors # and （-）.