In this paper,we study the category of corepresentations of a monoidal comonad.We show that it is a semisimple category if and only if the monoidal comonad is a cosemisipmle(coseparable)comonad,and it is a braided cat...In this paper,we study the category of corepresentations of a monoidal comonad.We show that it is a semisimple category if and only if the monoidal comonad is a cosemisipmle(coseparable)comonad,and it is a braided category if and only if the monoidal comonad admit a cobraided structure.At last,as an application,the braided structure and the semisimplicity of the Hom-comodule category of a monoidal Hom-bialgebra are discussed.展开更多
Let （H, α） be a monoidal Hom-Hopf algebra. In this paper, we will study the category of Hom-Yetter-Drinfeld modules. First, we show that the category of left-left Hom-Yetter-Drinfeld modules H^H HYD is isomorphic t...Let （H, α） be a monoidal Hom-Hopf algebra. In this paper, we will study the category of Hom-Yetter-Drinfeld modules. First, we show that the category of left-left Hom-Yetter-Drinfeld modules H^H HYD is isomorphic to the center of the category of left （H, α）-Hom-modules. Also, by the center construction, we get that the categories of left-left, left-right, right-left, and right-right Hom-Yetter-Drinfeld modules are isomorphic as braided monoidal categories. Second, we prove that the category of finitely generated projective left-left Hom-Yetter-Drinfeld modules has left and right duality.展开更多
基金the National Natural Science Foundation of China(Nos.11626138,11626139)the Natural Science Foundation of Shandong Province(No.ZR2016AQ03).
文摘In this paper,we study the category of corepresentations of a monoidal comonad.We show that it is a semisimple category if and only if the monoidal comonad is a cosemisipmle(coseparable)comonad,and it is a braided category if and only if the monoidal comonad admit a cobraided structure.At last,as an application,the braided structure and the semisimplicity of the Hom-comodule category of a monoidal Hom-bialgebra are discussed.
基金Acknowledgements The authors sincerely thank the referees for their valuable suggestions and comments on this paper. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11601486, 61272007. 11401534）.
文摘Let （H, α） be a monoidal Hom-Hopf algebra. In this paper, we will study the category of Hom-Yetter-Drinfeld modules. First, we show that the category of left-left Hom-Yetter-Drinfeld modules H^H HYD is isomorphic to the center of the category of left （H, α）-Hom-modules. Also, by the center construction, we get that the categories of left-left, left-right, right-left, and right-right Hom-Yetter-Drinfeld modules are isomorphic as braided monoidal categories. Second, we prove that the category of finitely generated projective left-left Hom-Yetter-Drinfeld modules has left and right duality.
