Structure sheaves of definable additive categories

DOI10.1016/j.jpaa.2009.11.003zbMath1203.18011OpenAlexW2036344564MaRDI QIDQ2268582

Ravi Rajani, M. Y. Prest

Publication date: 8 March 2010

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

Full work available at URL: http://eprints.maths.manchester.ac.uk/1194/1/shvdefcat3.pdf

zbMATH Keywords

dualitymodel theorymodule categoryGrothendieck categoryZiegler spectrumpreadditive categorydefinable subcategoryZiegler topology

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Injective modules, self-injective associative rings (16D50) Module categories in associative algebras (16D90) Abelian categories, Grothendieck categories (18E10) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20)

Related Items

The category of extensions and a characterisation of \(n\)-exangulated functors, Definable categories, Representation embeddings, interpretation functors and controlled wild algebras, Universal cohomology theories, The injective spectrum of a right Noetherian ring, Definable additive categories: purity and model theory, Enriched regular theories, Modules as exact functors, A monoidal analogue of the 2-category anti-equivalence between \(\mathbb{ABEX}\) and \(\mathbb{DEF} \), Modules with irrational slope over tubular algebras

Cites Work

• Remarks on elementary duality
• Model-theoretic imaginaries and coherent sheaves
• A theorem on Barr-exact categories, with an infinitary generalization
• De Morgan's law and the theory of fields
• Elementary torsion theories and locally finitely presented categories
• Sheaves in geometry and logic: a first introduction to topos theory
• Exactly definable categories
• Absolutely pure and flat modules and ``indiscrete rings
• The spectrum of a module category
• Definable additive categories: purity and model theory
• Imaginary modules
• Elementary Duality of Modules
• Locally finitely presented additive categories
• The Ziegler Spectrum of a Locally Coherent Grothendieck Category
• Functors on locally finitely presented additive categories
• Model-completions and modules
• Definability problems for modules and rings
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