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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm6509-12-2015,
author = {Shuangjian Guo and Xiaohui Zhang and Shengxiang Wang},
title = {Braided monoidal categories and Doi-Hopf modules for monoidal Hom-Hopf algebras},
journal = {Colloquium Mathematicae},
volume = {144},
year = {2016},
pages = {79-103},
zbl = {06545378},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6509-12-2015}
}
Shuangjian Guo; Xiaohui Zhang; Shengxiang Wang. Braided monoidal categories and Doi-Hopf modules for monoidal Hom-Hopf algebras. Colloquium Mathematicae, Tome 144 (2016) pp. 79-103. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6509-12-2015/