Quillen equivalence for chain homotopy categories induced by balanced pairs

Abstract

For a balanced pair $(\mathcal{X},\mathcal{Y})$ in an abelian category, we investigate when the chain homotopy categories $\mathbf{K}(\mathcal{X})$ and $\mathbf{K}(\mathcal{Y})$ are triangulated equivalent. To this end, we realize these chain homotopy categories as homotopy categories of certain model categories and give conditions that ensure the existence of a Quillen equivalence between the model categories in question. We further give applications to cotorsion triples, Gorenstein projective and Gorenstein injective modules, as well as pure projective and pure injective objects.

24 pages