Abstract
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.
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Acknowledgements
The work was partially supported by the National Natural Science Foundation of China (Nos. 11626138, 11626139), and the Natural Science Foundation of Shandong Province (No. ZR2016AQ03).
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Translated from Advances in Mathematics (China), 2017, 46(2): 221–233
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Zhang, X., Wu, H. The cosemisimplicity and cobraided structures of monoidal comonads. Front. Math. China 17, 485–499 (2022). https://doi.org/10.1007/s11464-022-1019-9
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DOI: https://doi.org/10.1007/s11464-022-1019-9