Cotorsion pairs and model structures on Ch(R)

DOI10.1017/S0013091510000489zbMath1238.13023MaRDI QIDQ3094677

Liu, Zhongkui, Gang Yang

Publication date: 25 October 2011

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

model structurescotorsion pairs(pre)covers(pre)envelopesprojective dimension of complexes

Mathematics Subject Classification ID

Related Items (33)

Dimension of complexes related to special Gorenstein projective precovers(II) ⋮ Cotorsion pairs and Cartan-Eilenberg categories ⋮ Gorenstein complexes and recollements from cotorsion pairs ⋮ Complete cohomology for complexes with finite Gorenstein AC-projective dimension ⋮ Totally acyclic complexes ⋮ Virtually Gorenstein rings and relative homology of complexes ⋮ Cut cotorsion pairs ⋮ Compactly generated triangulated subcategories of homotopy categories induced by cotorsion pairs ⋮ Auslander condition and Gorenstein rings ⋮ On the homotopy category of AC-injective complexes ⋮ Minimal semi-flat-cotorsion replacements and cosupport ⋮ A model structure approach to the Tate-Vogel cohomology ⋮ Ding injective envelopes in the category of complexes ⋮ Hereditary abelian model categories ⋮ HOMOLOGY THEORIES FOR COMPLEXES BASED ON FLATS ⋮ Relative cohomology of complexes based on cotorsion pairs ⋮ Recent Progress in Module Approximations ⋮ Tate cohomology for complexes with finite Gorenstein AC-injective dimension ⋮ Model Structures on Categories of Complexes Over Ding-Chen Rings ⋮ A QUILLEN MODEL STRUCTURE APPROACH TO HOMOLOGICAL DIMENSIONS OF COMPLEXES ⋮ Unnamed Item ⋮ CARTAN–EILENBERG GORENSTEIN PROJECTIVE COMPLEXES ⋮ When every pure ideal is projective ⋮ Derived equivalences induced by big cotilting modules ⋮ Gorenstein AC-projective dimension of unbounded complexes ⋮ Relative homological dimensions and Tate cohomology of complexes with respect to cotorsion pairs ⋮ Gorenstein projective complexes with respect to cotorsion pairs ⋮ Gorenstein Flat and Cotorsion Dimensions of Unbounded Complexes ⋮ Dimension and level of triangulated categories ⋮ GorensteinFP-Injective Dimension for Complexes ⋮ Applications of cotorsion pairs on triangulated categories ⋮ On Cotorsion Pairs of Chain Complexes ⋮ Model structures, recollements and duality pairs

Cites Work

• Homological dimensions of unbounded complexes
• Cotorsion pairs, model category structures, and representation theory
• Kaplansky classes and derived categories
• Cotorsion pairs and degreewise homological model structures
• How To Make Ext Vanish
• ALL MODULES HAVE FLAT COVERS
• Envelopes and Covers by Modules of FiniteFP-Injective and Flat Dimensions
• SPECIAL PRECOVERS IN COTORSION THEORIES
• The flat model structure on 𝐂𝐡(𝐑)
• !THE $\aleph_1$-PRODUCT OF DG-INJECTIVE COMPLEXES
• Envelopes and covers by modules of finite injective and projective dimensions
• Covers and envelopes in Grothendieck categories: Flat covers of complexes with applications

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