  The category-valued trace assigns to a bimodule category over a linear
monoidal category a linear category. It generalizes Drinfeld centers of
monoidal categories and the relative Deligne product of bimodule categories. In
this article, we study bimodule categories that are given as categories of
bicomodules over a Hopf algebra. Our main result is a representation-theoretic
realization of the category-valued trace as a category of generalized Hopf
bimodules.
