Hom-Hopf group coalgebras and braided T-categories obtained from Hom-Hopf algebras

The main aim of this paper is to provide new examples of braided T-categories in the sense of Turaev [Arabian J. Sci. Eng., Sect. C 33(2C), 483–503 (2008)]. For this purpose, we first introduce a class of new twisted Yetter-Drinfeld modules categories. Then, we construct a new braided T-category, generalizing the main constructions by Panaite and Staic [Isr. J. Math. 158, 349–366 (2007)]. Finally, we show that the new braided T-category in some conditions coincides with the representations of a certain Hom-Hopf group-coalgebra that we construct.