On algebraically exact categories and essential localizations of varieties

DOI10.1006/jabr.2000.8577zbMath1004.18006OpenAlexW2031250850MaRDI QIDQ5952407

Jiří Adámek, Jiří Rosický, Enrico M. Vitale

Publication date: 11 February 2003

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

Full work available at URL: https://doi.org/10.1006/jabr.2000.8577

zbMATH Keywords

additive categoriesalgebraically exact categoriesBarr-exactnessessential localizationsvarieties of finitary general algebras

Mathematics Subject Classification ID

Abelian categories, Grothendieck categories (18E10) Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) (18A30) Equational categories (18C05) Categories admitting limits (complete categories), functors preserving limits, completions (18A35) Accessible and locally presentable categories (18C35) Localization of categories, calculus of fractions (18E35)

Related Items

A characterisation of algebraic exactness ⋮ On sifted colimits in the presence of pullbacks ⋮ Definable categories ⋮ Toward a characterization of algebraic exactness. ⋮ Exactness of direct limits for abelian categories with an injective cogenerator ⋮ Algebra and local presentability: how algebraic are they? (A survey)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Localisation of locally presentable categories
• Cartesian closed exact completions
• Continuous categories and exponentiable toposes
• Introduction to extensive and distributive categories
• Localizations of algebraic categories. II
• Regular and exact completions
• Localizations of varieties and quasivarieties
• On locales of localizations
• A classification of accessible categories
• Some free constructions in realizability and proof theory
• Monads for which structures are adjoint to units
• The symmetric topos
• Limits in free coproduct completions
• Localizations of algebraic categories
• 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
• Sur quelques points d'algèbre homologique
• Des catégories abéliennes
• FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES
• The Full Imbedding Theorem
• Syntactic characterizations of various classes of locally presentable categories