A generalization of the Gabriel-Popescu theorem

DOI10.1016/j.jpaa.2003.11.016zbMath1051.18007OpenAlexW2055191027MaRDI QIDQ1878455

Wendy Lowen

Publication date: 19 August 2004

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2003.11.016

zbMATH Keywords

localizationGrothendieck categorypresheaf

Mathematics Subject Classification ID

Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Grothendieck topologies and Grothendieck topoi (18F10) Localization of categories, calculus of fractions (18E35)

Related Items (21)

Gabriel-Ulmer duality for topoi and its relation with site presentations ⋮ Exponentiable Grothendieck categories in flat algebraic geometry ⋮ Linearized topologies and deformation theory ⋮ The Popescu-Gabriel theorem for triangulated categories ⋮ Grothendieck categories as a bilocalization of linear sites ⋮ Moduli of non-commutative polarized schemes ⋮ Grothendieck enriched categories ⋮ Generalized lax epimorphisms in the additive case ⋮ A generalization of the Mitchell lemma: the Ulmer theorem and the Gabriel-Popescu theorem revisited ⋮ \(t\)-structures with Grothendieck hearts via functor categories ⋮ Additive Grothendieck pretopologies and presentations of tensor categories ⋮ Homological kernels of monoidal functors ⋮ Categories of modules, comodules and contramodules over representations ⋮ Abelian and derived deformations in the presence of \(\mathbb Z\)-generating geometric helices ⋮ Cohomology of exact categories and (non-)additive sheaves ⋮ Non-commutative deformations and quasi-coherent modules ⋮ Algebroid prestacks and deformations of ringed spaces ⋮ A classification of geometric morphisms and localizations for presheaf categories and algebraic categories ⋮ Torsion pairs in categories of modules over a preadditive category ⋮ Deformation theory of abelian categories ⋮ Hochschild cohomology of Abelian categories and ringed spaces

Cites Work

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• A quick proof of the Gabriel-Popesco theorem
• A simple proof of Gabriel and Popesco's theorem
• Seminar of algebraic geometry du Bois-Marie 1963--1964. Topos theory and étale cohomology of schemes (SGA 4). Vol. 1: Topos theory. Exp. I--IV
• Des catégories abéliennes

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