A homotopy 2-groupoid from a fibration.
Let be a monoidal Hom-Hopf algebra and a right -Hom-comodule algebra. We first introduce the notion of a relative Hom-Hopf module and prove that the functor from the category of relative Hom-Hopf modules to the category of right -Hom-modules has a right adjoint. Furthermore, we prove a Maschke type theorem for the category of relative Hom-Hopf modules. In fact, we give necessary and sufficient conditions for the functor that forgets the -coaction to be separable. This leads to a generalized...
We extend a result of M. M. Kapranov and Y. Manin concerning the Morita theory for linear operads. We also give a cyclic operad version of their result.