中文摘要：

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.

英文摘要：

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.