Some remarks about monoidal Hom-algebras

Abstract

In this paper, for ???? a strict braided monoidal category with tensor product ⊗, we improve the definition of Hom-associative algebra by removing the multiplicativity condition of the automorphism α. After that we state the close connection between the classical notions of (co)algebra, (co)module and Hopf algebra and the corresponding ones in the Hom-world. As a consequence we can study the questions about the Hom-world by passing to the classical one, and the main contribution of this paper is to illustrate the suitable procedure to move from one side to the other. Finally, we apply our techniques to get in the Hom setting some classical results about cleft and Galois extensions.