The General Induction Functors for the Category of Entwined Hom-Modules

Abstract

We find a sufficient condition for the category of entwined Hom-modules to be monoidal.
Moreover, we introduce morphisms between the underlying monoidal Hom-algebras and monoidal Hom-coalgebras, which give rise to functors between
the category of entwined Hom-modules, and we study tensor identities for monodial categories of entwined Hom-modules.
Finally, we give necessary and sufficient conditions for the general induction functor from $ {}\widetilde{\mathscr{H}}(\mathscr{M}_k)(\psi)^{C}_A$ to ${}\widetilde{\mathscr{H}}(\mathscr{M}_k)(\psi')^{C'}_{A'}$ to be separable.