Let $ 𝓗̃ (𝓜 _ {k})(H)^{C} _ {A} $ be the category of Doi Hom-Hopf modules, $ 𝓗̃ (𝓜 _ {k}) _ {A}
$ be the category of A-Hom-modules, and F be the forgetful functor from $ 𝓗̃ (𝓜 _ {k})(H)^{C} …

We prove a Maschke type theorem for the category of Doi–Hopf modules. In fact, we give
necessary and sufficient conditions for the functor that forgets the C-coaction to be …

We study when induction functors (and their adjoints) between categories of Doi-Hopf
modules and, more generally, entwined modules are separable, resp. Frobenius. We …

We study the following question: when is the right adjoint of the forgetful functor from the
category of $(H, A, C) $-Doi-Hopf modules to the category of $ A $-modules also a left …

We introduce the concept of relative Hom-Hopf modules and investigate their structure in a
monoidal category $ 𝓗̃ (ℳ_ {k}) $. More particularly, the fundamental theorem for relative …

Let π be a discrete group. Given a Doi-Hopf π-datum (H, A, C) and α∈ π, we give necessary
and sufficient conditions for the functor F (α) from the category of Doi-Hopf π-modules to the …

Let (H, α) be a monoidal Hom-Hopf algebra and (A, β) a right (H, α)-Homcomodule algebra.
We first introduce the notion of a relative Hom-Hopf module and prove that the functor F from …

We show that the two-sided two-cosided Hopf modules are in some case generalized Hopf
modules in the sense of Doi. Then the equivalence between two-sided two-cosided Hopf …

We give necessary and sufficient conditions for an induction functor (and its adjoint)
between categories of Doi‐Hopf modules to be separable. As a consequence, we find new …

In this paper, we introduce the concept of total integrals in the case of weak Hopf algebras,
which is a generalization of the total integral introduced by Menini and Militaru. We give two …