For an abelian category A we investigate when the stable categories Gorenstein projective A modules and Gorenstein injective A modules are triangulated equivalent. To this end, we realize these stable categories as homotopy categories of certain (non-trivial) model categories and give conditions on A that ensure the existence of a Quillen equivalence between the model categories in question. We also study when such a Quillen equivalence transfers from A to categories naturally associated to A.
Quillen equivalences for stable categories
Dalezios, Georgios
;Estrada, Sergio;
2018-01-01
Abstract
For an abelian category A we investigate when the stable categories Gorenstein projective A modules and Gorenstein injective A modules are triangulated equivalent. To this end, we realize these stable categories as homotopy categories of certain (non-trivial) model categories and give conditions on A that ensure the existence of a Quillen equivalence between the model categories in question. We also study when such a Quillen equivalence transfers from A to categories naturally associated to A.
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