%0 Journal Article %T Another construction of the braided $T$-category %A Tao Yang %J Mathematics %D 2014 %I arXiv %X This paper introduces group-cograded monoidal Hom-Hopf algebras, and shows that this kind of group-cograded monoidal Hom-Hopf algebras are monoidal Hom-Hopf algebras in the Turaev category introduced by Canepeel and De Lombaerde. Then we define the Yetter-Drinfeld category over a group-cograded monoidal Hom-Hopf algebra, and construct a new kind of braided $T$-categories. %U http://arxiv.org/abs/1409.6936v2