  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.
