Proper resolutions and Gorenstein categories

Let AA be an abelian category and CC an additive full subcategory of AA. We provide a method to construct a proper CC-resolution (resp. coproper CC-coresolution) of one term in a short exact sequence in AA from that of the other two terms. By using these constructions, we answer affirmatively an open question on the stability of the Gorenstein category G(C)G(C) posed by Sather-Wagstaff, Sharif and White; and also prove that G(C)G(C) is closed under direct summands. In addition, we obtain some criteria for computing the CC-dimension and the G(C)G(C)-dimension of an object in AA.