Coresolution Dimensions And Applications

Let C be an abelian category, X a subcategory of C. The X-coresolution di-mensions of objects in C are investigated in this paper. First of all, we discuss someproperties of X-coresolution dimensions of objects in C. Especially, using relativecohomology functor ExtnX, the equivalent characterizations of X-coresolution dimen-sions are given. Then we give some applications of X-coresolution dimensions. Atlast, we give a method to construct a new coresolving subcategory by coresolvingsubcategory.