Smash coproducts of monoidal comonads and Hom-entwining structures (Q2008600)

The paper under review is a new contribution to the theory of Hom-Hopf algebras. More precisely, after a section of preliminaries, in section 3 the authors give some necessary and sufficient conditions to prove the category of bicomodules of a comonad distributive law admit monoidal structure. In section 4, for two Hom-coalgebras \(B\) and \(H\), they describe the Hom-coalgebra structure of the smash coproduct \(B\otimes H\) and obtain the necessary and sufficient conditions for \(B\otimes H\) to be a Hom-bialgebra. Section 5 is focussed to study Hom-entwining structures. In particular, the authors introduce the notion of Hom-monoidal entwining structure and discuss the monoidal structure on the category of n-th Hom-entwined modules. Finally, in section 6, the authors consider the possible application of their theory into Hom-Doi-Hopf modules, Hom-Yetter-Drinfeld modules and Hom-Long dimodules.