Search results for "Quantaloid"

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On monadic quantale algebras: basic properties and representation theorems

2010

Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new structures.

Algebra and Number TheoryAlgebraic structureApplied MathematicsQuantaleAlgebraMathematics::LogicInterior algebraDistributive propertyComputer Science::Logic in Computer ScienceMathematics::Category TheoryBounded functionLattice (order)QuantaloidMathematicsDiscussiones Mathematicae - General Algebra and Applications
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From quantale algebroids to topological spaces: Fixed- and variable-basis approaches

2010

Using the category of quantale algebroids the paper considers a generalization of the classical Papert-Papert-Isbell adjunction between the categories of topological spaces and locales to partial algebraic structures. It also provides a single framework in which to treat the concepts of quasi, standard and stratified fuzzy topology.

Discrete mathematicsPure mathematicsBasis (linear algebra)LogicAlgebraic structureGeneralizationQuantaleTopological spaceAdjunctionArtificial IntelligenceMathematics::Category TheoryCategory of topological spacesQuantaloidMathematicsFuzzy Sets and Systems
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