Search results for "Universal property"

showing 3 items of 3 documents

Hypergraph functor and attachment

2010

Using an arbitrary variety of algebras, the paper introduces a fuzzified version of the notion of attachment in a complete lattice of Guido, to provide a common framework for the concept of hypergraph functor considered by different authors in the literature. The new notion also gives rise to a category of variable-basis topological spaces which is a proper supercategory of the respective category of Rodabaugh.

CombinatoricsFiber functorClosed categoryFunctorArtificial IntelligenceLogicMathematics::Category TheoryConcrete categoryUniversal propertyCone (category theory)Variety (universal algebra)Topological spaceMathematicsFuzzy Sets and Systems
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A fuzzification of the category of M-valued L-topological spaces

2004

[EN] A fuzzy category is a certain superstructure over an ordinary category in which ”potential” objects and ”potential” morphisms could be such to a certain degree. The aim of this paper is to introduce a fuzzy category FTOP(L,M) extending the category TOP(L,M) of M-valued L- topological spaces which in its turn is an extension of the category TOP(L) of L-fuzzy topological spaces in Kubiak-Sostak’s sense. Basic properties of the fuzzy category FTOP(L,M) and its objects are studied.

Pure mathematicsFunctorHomotopy categoryDiagram (category theory)Mathematics::General Mathematicslcsh:Mathematicslcsh:QA299.6-433lcsh:Analysislcsh:QA1-939GL-monoid(LM)-fuzzy topologyPower-set operators(LM)-interior operatorMathematics::Category TheoryCategory of topological spacesBiproductUniversal propertyGeometry and TopologyM-valued L-topologyCategory of setsL-fuzzy category(LM)-neighborhood systemMathematicsInitial and terminal objectsApplied General Topology
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Split extensions, semidirect product and holomorph of categorical groups

2006

Working in the context of categorical groups, we show that the semidirect product provides a biequivalence between actions and points. From this biequivalence, we deduce a two-dimensional classification of split extensions of categorical groups, as well as the universal property of the holomorph of a categorical group. We also discuss the link between the holomorph and inner autoequivalences.

Semidirect product18D05categorical groupsGroup (mathematics)split extensionssplit extension18D10Context (language use)18G5018D35AlgebraMathematics (miscellaneous)HolomorphMathematics::Category TheoryholomorphUniversal propertysemidirect productcategorical groupLink (knot theory)Categorical variableMathematics
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