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 Homcoalgebras, 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 ~H (Mk)(ψ)CA to ~H (Mk)(ψ')C'A' to be separable.
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