Search results for "2-category"

showing 3 items of 3 documents

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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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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Categories of lattice-valued sets as categories of arrows

2006

In this paper we introduce a category X(A) which is a generalization of the category of lattice-valued subsets of sets Set(JCPos) introduced by us earlier. We show the necessary and sufficient conditions for X(A) to be topological over XxA.

Discrete mathematicsHigher category theoryClosed categoryArtificial IntelligenceLogicMathematics::Category TheoryCategoryConcrete categoryCategory of topological spacesCategory of setsTopological category2-categoryMathematicsFuzzy Sets and Systems
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