Pure Injective and Absolutely Pure Sheaves

DOI10.1017/S0013091515000462zbMath1370.18011arXiv1307.1729WikidataQ114117477 ScholiaQ114117477MaRDI QIDQ2976218

Edgar E. Enochs, Sergio Estrada, Sinem Odabaşı

Publication date: 28 April 2017

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

Full work available at URL: https://arxiv.org/abs/1307.1729

zbMATH Keywords

coverenvelopelocally finitely presented categorylocal purityabsolutely pure sheafcategorical purityconcentrated schemepure injective sheaf

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Accessible and locally presentable categories (18C35) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Schemes and morphisms (14A15)

Related Items (10)

Cut cotorsion pairs ⋮ The tensor embedding for a Grothendieck cosmos ⋮ Purity and flatness in symmetric monoidal closed exact categories ⋮ Phantom covering ideals in categories without enough projective morphisms ⋮ Pure exact structures and the pure derived category of a scheme ⋮ Locally type \(\mathrm{FP}_n\) and \(n\)-coherent categories ⋮ Purity in categories of sheaves ⋮ Cartesian modules over representations of small categories ⋮ The pure derived category of quasi-coherent sheaves ⋮ On flat generators and Matlis duality for quasicoherent sheaves

Cites Work

• Relative homological algebra in the category of quasi-coherent sheaves.
• On the free product of associative rings
• Covers and directed colimits.
• Cup products in sheaf cohomology, pure injectives, and a substitute for projective resolutions
• Pure submodules
• Purity in functor categories
• Pure theories
• Covers in finitely accessible categories
• Classifying finite localizations of quasicoherent sheaves
• Locally finitely presented additive categories
• PURE-INJECTIVE ENVELOPES

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