The flat model structure on complexes of sheaves

DOI10.1090/S0002-9947-06-04157-2zbMath1094.55016MaRDI QIDQ3378454

James Gillespie

Publication date: 3 April 2006

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

model categoryflat cover

Mathematics Subject Classification ID

Ext and Tor, generalizations, Künneth formula (category-theoretic aspects) (18G15) Abstract and axiomatic homotopy theory in algebraic topology (55U35)

Related Items (21)

Exact model structures and recollements ⋮ Koszul-Tate resolutions as cofibrant replacements of algebras over differential operators ⋮ Cotorsion pairs and Cartan-Eilenberg categories ⋮ Homotopical algebraic context over differential operators ⋮ Six operations on dg enhancements of derived categories of sheaves ⋮ Model structures on the category of complexes of quiver representations ⋮ On Koszul–Tate resolutions and Sullivan models ⋮ Generalized tilting theory in functor categories ⋮ On exact categories and applications to triangulated adjoints and model structures ⋮ Hereditary abelian model categories ⋮ Model structures on exact categories ⋮ Cotorsion pairs and adjoint functors in the homotopy category of N-complexes ⋮ Purity and homotopy theory of coalgebras ⋮ The 𝑡-structure induced by an 𝑛-tilting module ⋮ Kaplansky classes and derived categories ⋮ Covers in finitely accessible categories ⋮ Deconstructibility and the Hill Lemma in Grothendieck categories ⋮ Kaplansky Classes and Cotorsion Theories of Complexes ⋮ Some adjoints in homotopy categories ⋮ Enlargement of (fibered) derivators ⋮ Cotorsion Dimension of Unbounded Complexes

Cites Work

• Flat covers of modules
• Cotorsion pairs, model category structures, and representation theory
• Relative homological algebra
• Homotopical algebra
• Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
• Sur quelques points d'algèbre homologique
• Model category structures on chain complexes of sheaves
• Flat covers and cotorsion envelopes of sheaves
• How To Make Ext Vanish
• ALL MODULES HAVE FLAT COVERS
• Flat Covers in the Category of Quasi-coherent Sheaves Over the Projective Line
• The flat model structure on 𝐂𝐡(𝐑)
• Covers and envelopes in Grothendieck categories: Flat covers of complexes with applications
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