Constructing Braided Hopf Algebras in Monoidal Hom-category

Abstract

In this paper, we first define the coquasitriangular monoidal Hom-Hopf algebras. Secondly, we present a method to construct braided monoidal Hom-Hopf algebras $\overline{B}$ and $\underline{B}$ in Yetter-Drinfeld category $\widetilde{\mathcal{H}}(_{H}\mathcal{YD}_1^{H})$ and $\widetilde{\mathcal{H}}(_{H}\mathcal{YD}_2^{H})$ respectively. As applications, we study some special cases in both module and comodule form for $(H, \xi_H)$ being quasitriangular and for $(H, \xi_H)$ being coquasitriangular respectively. Finally, we give some applications and examples of braided monoidal Hom-Hopf algebras in this article.