Homotopy category of projective complexes and complexes of Gorenstein projective modules.

DOI10.1016/J.JALGEBRA.2013.09.045zbMath1310.16005arXiv1202.1620OpenAlexW2085242440MaRDI QIDQ397869

Rasool Hafezi, Shokrollah Salarian, Javad Asadollahi

Publication date: 12 August 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.1620

zbMATH Keywords

precovershomotopy categoriesadjoint functorscategories of complexescompactly generated triangulated categoriesGorenstein projective complexes

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) Syzygies, resolutions, complexes and commutative rings (13D02) Syzygies, resolutions, complexes in associative algebras (16E05)

Related Items (4)

Compactly generated triangulated subcategories of homotopy categories induced by cotorsion pairs ⋮ On the existence of Gorenstein projective precovers ⋮ Applications of cotorsion pairs on triangulated categories ⋮ Constructing cogenerators in triangulated categories and Brown representability

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Totally acyclic complexes over noetherian schemes
• Stable \(t\)-structures and homotopy category of Gorenstein-projective modules
• Homotopy equivalences induced by balanced pairs
• Existence of Gorenstein projective resolutions and Tate cohomology
• The homotopy category of flat modules, and Grothendieck duality
• Gorenstein injective complexes of modules over Noetherian rings.
• Gorenstein homological dimensions.
• The homotopy category of complexes of projective modules
• Cotorsion pairs in \(\mathbf{C}(R-\text{Mod})\)
• On the homotopy categories of projective and injective representations of quivers
• Acyclicity versus total acyclicity for complexes over noetherian rings
• Approximations and endomorphism algebras of modules.
• Triangulated Categories
• Gorenstein projective and flat complexes over noetherian rings
• Localization theory for triangulated categories
• Gorenstein Projective, Injective, and Flat Complexes
• Gorenstein injective and projective complexes
• The homological theory of contravariantly finite subcategories:auslander-buchweitz contexts, gorenstein categories and (co-)stabilization
• The Grothendieck duality theorem via Bousfield’s techniques and Brown representability
• the stable derived category of a noetherian scheme

This page was built for publication: Homotopy category of projective complexes and complexes of Gorenstein projective modules.