Cartan-Eilenberg(Co) Proper Resolutions And Gorenstein Cartan-Eilenberg Category

Let(?)be an abelian category and(?)an additive full subcategory of(?).Base on the(co)proper(?)-resolution,Cartan-Eilenberg exact sequence(referred to as CE exact),we introduce the(co)proper CE-(?)-(co)resolution,provide a method to construct a(co)proper CE-(?)-(co)resolution in a short exact sequence,and give some relationship between CE-(?)-(co)resolution and the functor Homd(?)(-,-).Then,we introduce a new notion Gorenstein CE category,discusses the stability of the Gorenstein CE category.Finally,we study the(co)proper CE-(?)-(co)resolution and Gorenstein CE category.