Cotorsion pairs and degreewise homological model structures
نویسندگان
چکیده
منابع مشابه
Cotorsion pairs and model categories
The purpose of this paper is to describe a connection between model categories, a structure invented by algebraic topologists that allows one to introduce the ideas of homotopy theory to situations far removed from topological spaces, and cotorsion pairs, an algebraic notion that simultaneously generalizes the notion of projective and injective objects. In brief, a model category structure on a...
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We introduce the notion of a duality pair and demonstrate how the left half of such a pair is “often” covering and preenveloping. As an application, we generalize a result by Enochs et al. on Auslander and Bass classes, and we prove that the class of Gorenstein injective modules—introduced by Enochs and Jenda—is covering when the ground ring has a dualizing complex.
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Classical tilting theory generalizes Morita theory of equivalence of module categories. The key property – existence of category equivalences between large full subcategories of the module categories – forces the representing tilting module to be finitely generated. However, some aspects of the classical theory can be extended to infinitely generated modules over arbitrary rings. In this paper,...
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Let R be a Dedekind domain. In [6], Enochs’ solution of the Flat Cover Conjecture was extended as follows: (∗) If C is a cotorsion pair generated by a class of cotorsion modules, then C is cogenerated by a set. We show that (∗) is the best result provable in ZFC in case R has a countable spectrum: the Uniformization Principle UP implies that C is not cogenerated by a set whenever C is a cotorsi...
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ژورنال
عنوان ژورنال: Homology, Homotopy and Applications
سال: 2008
ISSN: 1532-0073,1532-0081
DOI: 10.4310/hha.2008.v10.n1.a12