Sweedler duality for Hom-algebras and Hom-modules

Abstract: The construction of Sweedler duality is an important tool in the theory of Hopf algebras over a field, which is a right adjoint to the dual algebra functor. In this paper, we study the Sweedler duality of Hom-algebras and their Hom-modules. We delve into the structure of Hom-coalgebras and derive the linear morphisms associated with them. Additionally, as an application, we present the (right) Hom-(co)module morphisms under the Sweedler duality.