Some Quillen Equivalences for Model Categories.

Let (L , A) be a complete duality pair. When R is a commutative ring, we prove a Quillen equivalence induced by a Sharp–Foxby adjunction on R-Mod associated to (L , A) between the Gorenstein (L , A) -projective and injective model categories, which results in a triangle equivalence between the stable category of Gorenstein (L , A) -projective modules and the stable category of Gorenstein (L , A) -injective modules. In addition, let R and R ′ be two (not necessarily commutative) rings. Under some conditions, we investigate the other Quillen equivalence between two Gorenstein (L , A) -projective model categories and prove that two stable categories consisting of all Gorenstein (L , A) -projective R-modules and all Gorenstein (L , A) -projective R ′ -modules respectively are triangle equivalent by Frobenius functors. [ABSTRACT FROM AUTHOR]