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The cosemisimplicity and cobraided structures of monoidal comonads
Published date: 15 Jun 2022
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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.
Key words: Comonads; braided cateogries; monoidal Hom-Hopf algebras
Xiaohui ZHANG , Hui WU . The cosemisimplicity and cobraided structures of monoidal comonads[J]. Frontiers of Mathematics in China, 2022 , 17(3) : 485 -499 . DOI: 10.1007/s11464-022-1019-9
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