Affine algebraic sets relative to an algebraic theory

DOI10.1007/BF01228678zbMath0931.18008MaRDI QIDQ1299935

Yves Diers

Publication date: 29 February 2000

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

zbMATH Keywords

dualityalgebraic theoryGalois theoryNullstellensatzalgebraic setsaffine algebraic geometryaffine setgeometrical categories

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Separable extensions, Galois theory (12F10) Equational categories (18C05) Categories in geometry and topology (18F99) Relevant commutative algebra (14A05)

Related Items (16)

The fundamental group as the structure of a dually affine space ⋮ Affine sets: the structure of complete objects and duality ⋮ Sierpinski object for affine systems ⋮ Topological systems as a framework for institutions ⋮ Sierpinski object for composite affine spaces ⋮ General affine adjunctions, Nullstellensätze, and dualities ⋮ A topologist's view of Chu spaces ⋮ Sobriety and spatiality in categories of lattice-valued algebras ⋮ Spaces modelled by an algebra on \([0,\infty \) and their complete objects] ⋮ Stratified categorical fixed-basis fuzzy topological spaces and their duality ⋮ Zariski closure, completeness and compactness ⋮ Topological geometrical categories ⋮ Characterization of a category for monoidal topology ⋮ Many for the price of one duality principle for affine sets ⋮ OnQ-sobriety ⋮ Finitely coordinated and finitely copresentable affine algebraic sets

Cites Work

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• Generating the algebraic theory of C(X)
• On the equational theory of \(C^*\)-algebras
• Categories of algebraic sets
• FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES

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