Cartesianness: topological spaces, uniform spaces, and affine schemes

DOI10.1016/0022-4049(82)90004-4zbMath0475.18011OpenAlexW1967613287MaRDI QIDQ1159756

Susan B. Niefield

Publication date: 1982

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(82)90004-4

zbMATH Keywords

projective modulelocally compactuniform spacecovering spacecommutative ringfunction spaceexponentialcartesian objects in non-cartesian closed categoriescategory of affine schemescategory of commutative K-algebrascompactly generated spaces

Mathematics Subject Classification ID

Function spaces in general topology (54C35) Projective and free modules and ideals in commutative rings (13C10) Uniform structures and generalizations (54E15) Closed categories (closed monoidal and Cartesian closed categories, etc.) (18D15)

Related Items (41)

On exponentiability of étale algebraic homomorphisms ⋮ Exponentiable functors between quantaloid-enriched categories ⋮ Fibrewise injectivity in order and topology ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Disconnectednesses and partial products ⋮ Unnamed Item ⋮ Exponentiable morphisms, partial products and pullback complements ⋮ Probability, valuations, hyperspace: Three monads on top and the support as a morphism ⋮ General function spaces, products and continuous lattices ⋮ Unnamed Item ⋮ A general framework for the semantics of type theory ⋮ T\(_{0}\)-reflection and injective hulls of fibre spaces ⋮ Unnamed Item ⋮ Exponentiability for maps means fibrewise core-compactness. ⋮ Continuous categories and exponentiable toposes ⋮ Unnamed Item ⋮ The glueing construction and double categories ⋮ Algebraic exponentiation for categories of Lie algebras ⋮ Unnamed Item ⋮ Exponentiable morphisms of domains ⋮ Lifting colimits in various categories ⋮ Cartesian closed coreflective subcategories of the category of topological spaces ⋮ Local homeomorphisms as the exponentiable morphisms in compact Hausdorff spaces ⋮ Cubical homotopical algebra and cochain algebras ⋮ Unnamed Item ⋮ Preservation of topological properties under exponentiation ⋮ Open maps, colimits, and a convenient category of fibre spaces ⋮ Unnamed Item ⋮ Locally compact path spaces ⋮ Unnamed Item ⋮ Exponentiable maps and triquotients in \({\mathcal T}op\) ⋮ Exponentiable monomorphisms in categories of domains ⋮ Exponentiation in \({\mathcal V}\)-categories ⋮ Unnamed Item ⋮ EXPONENTIABLE MONOMORPHISMS ⋮ The universal exponentiable arrow ⋮ Fibrewise smash product and fibrewise mapping spaces ⋮ Injectivity and sections ⋮ Injective topological fibre spaces ⋮ Adjoints to tensor for graded algebras and coalgebras

Cites Work

• Productivity of coreflective subcategories of uniform spaces
• The Spectral Theory of Distributive Continuous Lattices
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Cartesianness: topological spaces, uniform spaces, and affine schemes