中文摘要：

设C是κ-线性范畴，M是C-C双模，定义κ-线性平凡扩张范畴C’=C M，首先证明其为平凡扩张代数的自然推广，其次证明左C’-模范畴等价于左C-模范畴关于张量函子M c-的右平凡扩张范畴（C-Mod） （M c-），推广了经典的平凡扩张代数的模范畴理论．并将此结论应用到女一线性三角矩阵范畴，重新刻画其模范畴的结构．

英文摘要：

In this paper, the trivial extension of a κ-linear category is introduced, which is a generalization of the trivial extension of an algebra. Let C＇ = C M be the trivial extension of a κ-linear category C by a C-bimodule M. It is proved that the left module cate- gory C＇-Mod is equivalent to the right trivial extension category （C-Mod） （M c-） ,which generalizes the classical theory on module category of trivial extensions of algebras. When,applying the above result to the k-linear triangular matrix category, it is easy to de- scribe the structure of its module category.