Search results for "Enriched category"

showing 5 items of 5 documents

On the category Set(JCPos)

2006

Category Set(JCPos) of lattice-valued subsets of sets is introduced and studied. We prove that it is topological over SetxJCPos and show its ''natural'' coalgebraic subcategory.

SubcategoryDiscrete mathematicsLogicConcrete categoryTopological categoryClosed categoryMathematics::K-Theory and HomologyArtificial IntelligenceMathematics::Category TheoryCategoryCategory of topological spacesEnriched categoryCategory of setsMathematicsFuzzy Sets and Systems
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Some remarks on the category SET(L), part III

2004

This paper considers the category SET(L) of L-subsets of sets with a fixed basis L and is a continuation of our previous investigation of this category. Here we study its general properties (e.g., we derive that the category is a topological construct) as well as some of its special objects and morphisms.

Discrete mathematicsDiagram (category theory)General MathematicsConcrete categoryCategory of groupsL-set; category of L-subsets of sets; topological construct; topos; special morphism; special objectCombinatoricsClosed categoryMathematics::Category TheoryCategory of topological spacesCategory of setsEnriched category2-categoryMathematicsGlasnik matematički
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Topological systems and Artin glueing

2012

Abstract Using methods of categorical fuzzy topology, the paper shows a relation between topological systems of S. Vickers and Artin glueing of M. Artin. Inspired by the problem of interrelations between algebra and topology, we show the necessary and sufficient conditions for the category, obtained by Artin glueing along an adjoint functor, to be (co)algebraic and (co)monadic, incorporating the respective result of G. Wraith. As a result, we confirm the algebraic nature of the category of topological systems, showing that it is monadic.

Artin approximation theoremClosed categoryAlgebraic structureMathematics::Category TheoryGeneral MathematicsConcrete categoryCategory of topological spacesVariety (universal algebra)TopologyEnriched categoryConductorMathematicsMathematica Slovaca
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Category, Measure, Inductive Inference: A Triality Theorem and Its Applications

2002

The famous Sierpinski-Erdos Duality Theorem [Sie34b, Erd43] states, informally, that any theorem about effective measure 0 and/or first category sets is also true when all occurrences of "effective measure 0" are replaced by "first category" and vice versa. This powerful and nice result shows that "measure" and "category" are equally useful notions neither of which can be preferred to the other one when making formal the intuitive notion "almost all sets." Effective versions of measure and category are used in recursive function theory and related areas, and resource-bounded versions of the same notions are used in Theory of Computation. Again they are dual in the same sense.We show that in…

Discrete mathematicsCategoryConcrete categoryCategory of setsCategory theoryEnriched categoryPrevalent and shy setsMathematics2-categoryDual (category theory)
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On a generalization of Goguen's category Set(L)

2007

The paper considers a category which generalizes Goguen's category Set(L) of L-fuzzy sets with a fixed basis L. We show the necessary and sufficient conditions for the generalized category to be a quasitopos and consider additional inner structure supplied by the latter property.

Discrete mathematicsClosed categoryArtificial IntelligenceLogicDiagram (category theory)Complete categoryMathematics::Category TheoryCategoryConcrete categoryCategory of setsEnriched categoryMathematicsTopological categoryFuzzy Sets and Systems
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