张量余单子的余半单性与余辫子结构  

The Cosemisimplicity and Cobraided Structure of Monoidal Comonads

作　　者：张晓辉[1] 吴慧[1,2] ZHANG Xiaohui WU Hui(School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, 273165, P. R. China School of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu, 210094, P. R. China)

机构地区：[1]曲阜师范大学数学科学学院,曲阜山东273165 [2]南京理工大学理学院,南京江苏210094

出　　处：《数学进展》2017年第2期221-233,共13页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.11371088);山东省自然科学基金(No.ZR2016AQ03);国家专项基金数学天元基金(No.11626138;No.11626139);曲阜师范大学科技计划(No.xkj201514)

摘　　要：本文研究了张量余单子的余半单性和余表示范畴,给出了其余半单性和余可裂性的等价性定理.并证明了其余表示范畴是辫子范畴当且仅当该张量余单子是余辫子的.作为应用研究了张量型Hom-双代教的Hom-余模范畴的半单性和辫子结构.In this paper, we study the cosemisimple structure and the corepresentations of a monoidal comonad, and give the necessary and sufficient conditions for the monoidal comonad being cosemisimple and coseparable. We also show that the corepresentation category of a monoidal comonad is a braided category if and only if the monoidal comonad admits a cobraided structure. Finally, as an application, the braided structure and the semisimplicity of the Hom- comodule category of a monoidal Hom-bialgebra are discussed.

关 键 词：余单子 辫子张量范畴 张量型Hom-双代数 

分 类 号：O154.1[理学—数学]