Hopf bimodules for bialgebroids (opens in new tab)

Generalising a result for Hopf algebras, we not only define the four possible types of Hopf modules in the bialgebroid setting but also yield the notion of two-sided two-cosided Hopf modules, also known as Hopf bimodules or tetramodules, in this realm. By explicitly formulating a fundamental theorem for Hopf modules via the concept of Hopf-Galois comodules, we prove that the category of Hopf bimodules can be endowed with the structure of a (...