  Any finite-dimensional Hopf algebra H is Frobenius and the stable category of
H-modules is triangulated monoidal. To H-comodule algebras we assign
triangulated module-categories over the stable category of H-modules. These
module-categories are generalizations of homotopy and derived categories of
modules over a differential graded algebra. We expect that, for suitable H, our
construction could be a starting point in the program of categorifying quantum
invariants of 3-manifolds.
