Quillen equivalence of singular model categories

zbMATH Open1449.18007arXiv1901.02137MaRDI QIDQ5209092

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Publication date: 22 January 2020

Abstract: Let $R$ be a left-Gorenstein ring. We show that there is a Quillen equivalence between singular contraderived model category and singular coderived model category. Consequently, an equivalence between the homotopy category of exact complexes of projective modules and the homotopy category of exact complexes of injective modules is given.

Full work available at URL: https://arxiv.org/abs/1901.02137

zbMATH Keywords

Quillen equivalencemodel categoryleft-Gorenstein ring

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Chain complexes (category-theoretic aspects), dg categories (18G35) Homotopical algebra, Quillen model categories, derivators (18N40) Derived categories, triangulated categories (18G80)

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