The authors give conditions ensuring Quillen equivalence between model categories whose homotopy categories are the chain homotopy categories of a balanced pair, with applications to cotorsion triples and Gorenstein projective and injective modules.
Murfet, Derived categories, Part I, (2006), avaliable from http://therisingsea.org/notes /DerivedCategories.pdf
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Quillen equivalence for chain homotopy categories induced by balanced pairs
The authors give conditions ensuring Quillen equivalence between model categories whose homotopy categories are the chain homotopy categories of a balanced pair, with applications to cotorsion triples and Gorenstein projective and injective modules.