Cotorsion pairs in \(\mathbf{C}(R-\text{Mod})\)

DOI10.1216/RMJ-2012-42-6-1787zbMath1268.18011MaRDI QIDQ1945724

Juan Rada, Overtoun M. G. Jenda, Edgar E. Enochs, Diego Bravo, Alina C. Iacob

Publication date: 9 April 2013

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1361800606

zbMATH Keywords

homotopy categorymodel structuresadjoint functorscotorsion pairscomplexes of modules

Mathematics Subject Classification ID

Abstract and axiomatic homotopy theory in algebraic topology (55U35)

Related Items (16)

Gorenstein complexes and recollements from cotorsion pairs ⋮ Homological dimensions and abelian model structures on chain complexes ⋮ Auslander's formula: variations and applications ⋮ Derived, coderived, and contraderived categories of locally presentable abelian categories ⋮ Homotopy category of projective complexes and complexes of Gorenstein projective modules. ⋮ On the homotopy category of AC-injective complexes ⋮ On K-absolutely pure complexes ⋮ On exact categories and applications to triangulated adjoints and model structures ⋮ Cotorsion pairs and adjoint functors in the homotopy category of N-complexes ⋮ Model structures and relative Gorenstein flat modules and chain complexes ⋮ A cotorsion theory in the homotopy category of flat quasi-coherent sheaves ⋮ Kaplansky Classes and Cotorsion Theories of Complexes ⋮ Singular compactness and definability for \(\Sigma\)-cotorsion and Gorenstein modules ⋮ TWO DESCRIPTIONS OF RELATIVE DERIVED CATEGORIES ⋮ On Cotorsion Pairs of Chain Complexes ⋮ Applications of hyperhomology to adjoint functors

Cites Work

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• Projective modules
• Some adjoints in homotopy categories
• Cotorsion pairs, model category structures, and representation theory
• Cotorsion pairs and degreewise homological model structures
• Approximations and endomorphism algebras of modules.
• Covers and envelopes in Grothendieck categories: Flat covers of complexes with applications

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