Algebra and local presentability: how algebraic are they? (A survey)

DOI10.1515/tmj-2017-0113zbMath1387.18010OpenAlexW2784199065MaRDI QIDQ680309

Jiří Rosický, Jiří Adámek

Publication date: 23 January 2018

Published in: Tbilisi Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/tmj-2017-0113

zbMATH Keywords

dualityalgebraic theoryvarietylocally finitely presentable categoryalgebraic functorsifted categories

Mathematics Subject Classification ID

Equational categories (18C05) Theories (e.g., algebraic theories), structure, and semantics (18C10) Accessible and locally presentable categories (18C35) Equational classes, universal algebra in model theory (03C05) Categories of algebras (08C05)

Cites Work

• Regularity of ultrafilters and the core model
• Continuous categories and exponentiable toposes
• Monoidal bicategories and Hopf algebroids
• Beck's theorem for pseudo-monads
• Monads for which structures are adjoint to units
• A characterisation of algebraic exactness
• On the duality between varieties and algebraic theories
• Lokal präsentierbare Kategorien. (Locally presentable 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
• Filter Monads, Continuous Lattices and Closure Systems
• FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES
• On algebraically exact categories and essential localizations of varieties
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