Chains of equivalent model structures arise from cotorsion pairs in extriangulated categories under completeness assumptions, with homotopy categories triangulated-equivalent to a common stable category, recovering Gorenstein results and adding derived-category examples.
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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.
In an abelian category with a Hovey triple (Q, W, R), the subclass Q_n of objects with Q-resolution dimension ≤ n itself forms a hereditary Hovey triple, yielding a model structure on Qcoh(X) with bounded Gorenstein dimensions.
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Chains of model structures arising from cotorsion pairs on extriangulated categories
Chains of equivalent model structures arise from cotorsion pairs in extriangulated categories under completeness assumptions, with homotopy categories triangulated-equivalent to a common stable category, recovering Gorenstein results and adding derived-category examples.
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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.
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Approximations and Hovey triples by objects of finite homological dimensions: Applications to sheaves
In an abelian category with a Hovey triple (Q, W, R), the subclass Q_n of objects with Q-resolution dimension ≤ n itself forms a hereditary Hovey triple, yielding a model structure on Qcoh(X) with bounded Gorenstein dimensions.