中文摘要：

本文首先引入了一类新的范畴A YD H G,这个范畴是一簇范畴{A YD H（α,β）}（α,β）∈G的非交并,获得了范畴{A YD H（α,β）}（α,β）∈G是一个辫子T-范畴当且仅当（A,H,Q）是一个G-偶结构,推广了2005年Panaite和Staic的主要结论.最后,当H是有限维时,构造了一个拟三角T-余代数{A#H＊（α,β）}（α,β）∈G,它的表示范畴与{A YD H（α,β）}（α,β）∈G是同构的.

英文摘要：

In this paper, we first introduce a class oi new A YD H G junion of family of categories {A YD H（α,β）}（α,β）∈GThen we mainly show that the category{A YD H（α,β）}（α,β）∈G forms a braided T-category if and only if there is a map such that （A, H, Q）is a G-double structure, generalizing the main constructions by Fanaite and Stale （2005）. Finally,when H is finite-dimensional we construct a quasitriangular T-coalgebra {A#H＊（α,β）}（α,β）∈Gec,such that {A#H＊（α,β）}（α,β）∈Gis isomorphic to the representation category of the quasitriangularT-coalgebra {A YD H（α,β）}（α,β）∈G.