A monoidal structure on the category of relative hopf modules

摘要

Let B be a bialgebra, and A be a left B-comodule algebra in a braided monoidal category C, and assume that A is also a coalgebra, with a not-necessarily associative or unital left B-action. Then we can define a right A-action on the tensor product of two relative Hopf modules, and this defines a monoidal structure on the category of relative Hopf modules if and only if A is a bialgebra in the category of left YetterDrinfeld modules over B. Some examples are given.