中文摘要：

给出了Abelian范畴A和复形范畴Ch（A）中X-Gorenstein内射对象及YX-Gorenstein内射对象的定义,其中XA,YX={Y∈Ch（A）｜Y是正合复形且KerdnY∈X}。研究了这两类Gorenstein内射对象的同调性质及它们的区别和联系。证明了若X是包含所有内射对象的自正交的满子范畴,则X∈Ch（A）是YX-Gorenstein内射的当且仅当Xi都是X-Gorenstein内射的。在此基础上研究了两类范畴中X-Gorenstein内射维数和YX-Gorenstein内射维数以及它们之间的关系。在一定的条件下,YX-G I dim（X）=Sup{X-G I dim（Xi）｜i∈Z}。

英文摘要：

Let A be an abelian category with enough injective objects and X a full subcategory of A. The definitions of X-Gorenstein injective object and YX-Gorenstein injective object are given,where YX= { Y∈Ch（ A） ｜ Y is acyclic and KerdnY∈X. Under certain conditions,these two Gorenstein injective objects are related in a nice way. In particular,if I（ A） X,X∈Ch（ A） is YX-Gorenstein injective if and only if Xiis X-Gorenstein injective for each i,when X is a self-orthogonal class. Subsequently,the relationships between X-Gorenstein injective dimension and YX-Gorenstein injective dimension are considered.