From quantale algebroids to topological spaces: fixed- and variable-basis approaches
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Publication:969582
DOI10.1016/j.fss.2010.01.004zbMath1193.54010OpenAlexW1968989621MaRDI QIDQ969582
Publication date: 7 May 2010
Published in: Fuzzy Sets and Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.fss.2010.01.004
stratified spacequantaloidsobrietyspatiality(fixed-basis, variable-basis) topological space(variable-basis) topological systemfuzzy object in a categoryquantale (algebra, algebroid, module)soberificationspectrum adjunction
Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Fuzzy topology (54A40) Categorical methods in general topology (54B30) Frames, locales (06D22) Special categories (18B99) Quantales (06F07)
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Cites Work
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- Unnamed Item
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- A categorical accommodation of various notions of fuzzy topology
- Free quantaloids
- 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
- Sobriety and spatiality in varieties of algebras
- Fuzzy sets and sheaves. I: Basic concepts
- Fuzzy sets and sheaves. II: Sheaf-theoretic foundations of fuzzy set theory with applications to algebra and topology
- Relationship of algebraic theories to powerset theories and fuzzy topological theories for lattice-valued mathematics
- Fuzzy points and attachment
- Variable-basis topological systems versus variable-basis topological spaces
- Rough sets and fuzzy sets
- Basic notions for fuzzy topology. II
- Concrete categories and infinitary languages
- Fuzzy topological spaces and fuzzy compactness
- Topological and algebraic structures in fuzzy sets. A handbook of recent developments in the mathematics of fuzzy sets
- Free adjunction of morphisms
- A comparative study of fuzzy rough sets
- Applications of localic separation axioms, compactness axioms, representations, and compactifications to poslat topological spaces
- Topological theories and closed objects
- On the category \(Q\)-\textbf{Mod}
- L-fuzzy sets
- Modules with decompositions that complement direct summands
- Algebraic and Categorical Aspects of Quantales
- ROUGH FUZZY SETS AND FUZZY ROUGH SETS*
- Lattice Theory for Rough Sets
- Relative injectivity as cocompleteness for a class of distributors
- Functorial relationships between lattice-valued topology and topological systems
- Rough sets
- POWERSET OPERATOR BASED FOUNDATION FORPOINT-SET LATTICE-THEORETIC (POSLAT) FUZZY SET THEORIES and TOPOLOGIES
- Category Theory
- Fuzzy sets
- Categories of $V$-sets
- Relational algebras
- Atomless Parts of Spaces.
- Fuzzy topological spaces
