Radford (m, n)-biproduct and -Yetter-Drinfeld category

摘要

In this article, firstly, we introduce the notions of m-smash product monoidal Hom-algebra and n-smash coproduct monoidal Hom-coalgebra Furthermore, the necessary and sufficient conditions for and on to be a monoidal Hom-bialgebra structure are derived, where the conditions are equivalent to that is a bialgebra in the -Yetter-Drinfeld category. Secondly, we prove that the category is a braided monoidal category. At last, we give two mapping descriptions of Radford (0, 0)-biproduct.