Sobriety and spatiality in varieties of algebras

DOI10.1016/j.fss.2008.02.010zbMath1177.54004OpenAlexW1967370057MaRDI QIDQ835242

Sergey A. Solovyov

Publication date: 28 August 2009

Published in: Fuzzy Sets and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.fss.2008.02.010

zbMATH Keywords

varietyt-normquantalequantale modulelocalic algebraquantale algebra\(\Omega \)-algebra\(Q\)-powerset\(Q\)-Sierpiński space\(Q\)-sober \(Q\)-space\(Q\)-space\(Q\)-spatial localic algebra\(Q\)-topologystratified \(Q\)-space

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Fuzzy topology (54A40) Special categories (18B99) Quantales (06F07)

Related Items (29)

Fundamental duality of abstract categories and its applications ⋮ Lattice-valued preordered sets as lattice-valued topological systems ⋮ On injective objects and existence of injective hulls in 𝑄-TOP/(𝑌, 𝜎) ⋮ Sierpinski object for affine systems ⋮ Many valued topologies on L-sets ⋮ Sierpinski object for composite affine spaces ⋮ Constructing \(Q\)-algebras from \(Q\)-modules ⋮ Hypergraph functor and attachment ⋮ On limits and colimits of variety-based topological systems ⋮ On a generalization of the concept of state property system ⋮ A survey of fuzzifications of frames, the Papert-Papert-Isbell adjunction and sobriety ⋮ Categorical foundations of variety-based topology and topological systems ⋮ Editorial ⋮ Category-theoretic fuzzy topological spaces and their dualities ⋮ Categorically algebraic topology versus universal topology ⋮ A characterization of the category \(Q\)-\(\mathbf{TOP}\) ⋮ Unnamed Item ⋮ Composite variety-based topological theories ⋮ Sobriety and spatiality in categories of lattice-valued algebras ⋮ From quantale algebroids to topological spaces: fixed- and variable-basis approaches ⋮ Fuzzy algebras as a framework for fuzzy topology ⋮ Generalized fuzzy topology versus non-commutative topology ⋮ Variable-basis topological systems versus variable-basis topological spaces ⋮ Stratified categorical fixed-basis fuzzy topological spaces and their duality ⋮ Exponential \(Q\)-topological spaces ⋮ ON Q-BITOPOLOGICAL SPACES ⋮ OnQ-sobriety ⋮ A characterization of the category FCS ⋮ On fuzzification of topological categories

Cites Work

• Point-set lattice-theoretic topology
• Category theoretic aspects of chain-valued frames. I: Categorical and presheaf theoretic foundations
• Category theoretic aspects of chain-valued frames. II: Applications to lattice-valued topology
• Relationship of algebraic theories to powerset theories and fuzzy topological theories for lattice-valued mathematics
• Fuzzy topologies and topological space objects in a topos
• \(FTS_ 0:\) The epireflective hull of the Sierpinski object in FTS
• A representation theorem for quantales
• Fuzzy topological spaces and fuzzy compactness
• Topological and algebraic structures in fuzzy sets. A handbook of recent developments in the mathematics of fuzzy sets
• Handbook of algebra. Volume 3
• The fuzzy Tychonoff theorem
• Lineare Algebra. (Linear algebra).
• Applications of localic separation axioms, compactness axioms, representations, and compactifications to poslat topological spaces
• On the category \(Q\)-\textbf{Mod}
• L-fuzzy sets
• Modules with decompositions that complement direct summands
• An extension of the Galois theory of Grothendieck
• Quantales, observational logic and process semantics
• Fuzzy sets
• Atomless Parts of Spaces.
• The Theory of Representation for Boolean Algebras
• Applications of the Theory of Boolean Rings to General Topology
• Topological representations of distributive lattices and Brouwerian logics
• Fuzzy topological spaces
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