A monoidal structure on the category of relative Hopf modules

Let $B$ be a bialgebra, and $A$ a left $B$-comodule algebra in a braided monoidal
category $\Cc$, 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 Yetter-Drinfeld modules over $B$. Some examples are given.

Publication year:2012

Keywords:Monoidal category, Relative Hopf module, Yetter-Drinfeld module, braided bialgebra