You, Miman; Wang, Shuanhong Constructing braided Hopf algebras in monoidal Hom-category. (English) Zbl 1357.16051 Taiwanese J. Math. 20, No. 6, 1203-1230 (2016). Summary: 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. MSC: 16T05 Hopf algebras and their applications 18D10 Monoidal, symmetric monoidal and braided categories (MSC2010) Keywords:monoidal Hom-Hopf algebra; braided monoidal Hom-Hopf algebra; Yetter-Drinfeld module PDFBibTeX XMLCite \textit{M. You} and \textit{S. Wang}, Taiwanese J. Math. 20, No. 6, 1203--1230 (2016; Zbl 1357.16051) Full Text: DOI