Braided monoidal categories and Doi–Hopf modules for monoidal Hom-Hopf algebras

Volume 143 / 2016

Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang Colloquium Mathematicum 143 (2016), 79-103 MSC: Primary 16T05. DOI: 10.4064/cm6509-12-2015 Published online: 3 December 2015


We continue our study of the category of Doi Hom-Hopf modules introduced in [Colloq. Math., to appear]. We find a sufficient condition for the category of Doi Hom-Hopf modules to be monoidal. We also obtain a condition for a monoidal Hom-algebra and monoidal Hom-coalgebra to be monoidal Hom-bialgebras. Moreover, we introduce morphisms between the underlying monoidal Hom-Hopf algebras, Hom-comodule algebras and Hom-module coalgebras, which give rise to functors between the category of Doi Hom-Hopf modules, and we study tensor identities for monodial categories of Doi Hom-Hopf modules. Furthermore, we construct a braiding on the category of Doi Hom-Hopf modules. Finally, as an application of our theory, we get a braiding on the category of Hom-modules, on the category of Hom-comodules, and on the category of Hom-Yetter–Drinfeld modules.


  • Shuangjian GuoDepartment of Mathematics
    Zhejiang University
    Hangzhou, 310027, P.R. China
    School of Mathematics and Statistics
    Guizhou University of Finance and Economics
    Guiyang, 550025, P.R. China
  • Xiaohui ZhangSchool of Mathematical Sciences
    Qufu Normal University
    Qufu 273165, P.R. China
  • Shengxiang WangSchool of Mathematics and Finance
    Chuzhou University
    Chuzhou 239000, P.R. China
    Department of Mathematics
    Nanjing University
    Nanjing 210093, P.R. China

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