Geodesic
Braided monoidal categories and Doi–Hopf modules for monoidal Hom-Hopf algebras
Shuangjian Guo 1   ; Xiaohui Zhang 2   ; Shengxiang Wang 3
1 Department of Mathematics Zhejiang University Hangzhou, 310027, P.R. China and School of Mathematics and Statistics Guizhou University of Finance and Economics Guiyang, 550025, P.R. China
2 School of Mathematical Sciences Qufu Normal University Qufu 273165, P.R. China
3 School of Mathematics and Finance Chuzhou University Chuzhou 239000, P.R. China and Department of Mathematics Nanjing University Nanjing 210093, P.R. China
Colloquium Mathematicum, Tome 143 (2016) no. 1, pp. 79-103 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm6509-12-2015
Keywords: continue study category doi hom hopf modules introduced colloq math appear sufficient condition category doi hom hopf modules monoidal obtain condition monoidal hom algebra monoidal hom coalgebra monoidal hom bialgebras moreover introduce morphisms between underlying monoidal hom hopf algebras hom comodule algebras hom module coalgebras which rise functors between category doi hom hopf modules study tensor identities monodial categories doi hom hopf modules furthermore construct braiding category doi hom hopf modules finally application theory get braiding category hom modules category hom comodules category hom yetter drinfeld modules

Shuangjian Guo  1   ; Xiaohui Zhang  2   ; Shengxiang Wang  3

1 Department of Mathematics Zhejiang University Hangzhou, 310027, P.R. China and School of Mathematics and Statistics Guizhou University of Finance and Economics Guiyang, 550025, P.R. China
2 School of Mathematical Sciences Qufu Normal University Qufu 273165, P.R. China
3 School of Mathematics and Finance Chuzhou University Chuzhou 239000, P.R. China and Department of Mathematics Nanjing University Nanjing 210093, P.R. China 
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Shuangjian Guo; Xiaohui Zhang; Shengxiang Wang. Braided monoidal categories and Doi–Hopf modules for monoidal Hom-Hopf algebras. Colloquium Mathematicum, Tome 143 (2016) no. 1, pp. 79-103. doi: 10.4064/cm6509-12-2015

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