Exactly definable categories

DOI10.1006/jabr.1997.7252zbMath0917.18005OpenAlexW1992574460MaRDI QIDQ1270359

Henning Krause

Publication date: 2 August 1999

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

Full work available at URL: https://doi.org/10.1006/jabr.1997.7252

zbMATH Keywords

abelian categoryexact functorsfinite lengthZiegler spectrumartinianendo-finiteendocategoryexactly definable categoriespure-exactpure-injective

Mathematics Subject Classification ID

Abelian categories, Grothendieck categories (18E10)

Related Items (32)

Pure Goldie dimensions for exactly definable categories ⋮ Maranda’s theorem for pure-injective modules and duality ⋮ Unnamed Item ⋮ On the Pure-injectivity Profile of a Ring ⋮ The phantom cover of a module. ⋮ Torsion pairs in silting theory ⋮ Chase's lemma and its context ⋮ Flat endofinite modules, prime ideals, and duality. ⋮ Definable categories ⋮ Cotilting with balanced big Cohen-Macaulay modules ⋮ Purity in compactly generated derivators and t-structures with Grothendieck hearts ⋮ Baer-Kaplansky classes in Grothendieck categories and applications ⋮ Representation embeddings, interpretation functors and controlled wild algebras ⋮ Reflective and coreflective subcategories ⋮ Cotilting sheaves over weighted noncommutative regular projective curves ⋮ Approximations and adjoints in homotopy categories ⋮ PURE SEMISIMPLE FINITELY ACCESSIBLE CATEGORIES AND HERZOG'S CRITERION ⋮ Covers in finitely accessible categories ⋮ Exact categories and infinite tilting ⋮ DEFINABLE SUBCATEGORIES OVER PURE SEMISIMPLE RINGS ⋮ Uniqueness of uniform decompositions in exact categories ⋮ Additive categories of locally finite representation type ⋮ Structure sheaves of definable additive categories ⋮ Contravariant functors on the category of finitely presented modules. ⋮ Definable additive categories: purity and model theory ⋮ Gruson-Jensen Duality for Idempotent Rings ⋮ COHOMOLOGICAL LENGTH FUNCTIONS ⋮ Embeddings of Exactly Definable and Finitely Accessible Additive Categories into Freyd Categories ⋮ Modules as exact functors ⋮ Multisorted modules and their model theory ⋮ Modules with irrational slope over tubular algebras ⋮ Endofiniteness in stable homotopy theory

Cites Work

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• The spectrum of a locally coherent category
• Model theory of modules
• The Krull-Gabriel dimension of the representation theory of a tame hereditary Artin algebra and applications to the structure of exact sequences
• Representation embeddings and the Ziegler spectrum
• Stable equivalence preserves representation type
• Ultraproducts in the theory of models
• The spectrum of a module category
• Locally finitely presented additive categories
• Functors on locally finitely presented additive categories
• Generic Modules Over Artin Algebras
• Des catégories abéliennes

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