Search results for "Category of groups"

showing 2 items of 2 documents

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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External derivations of internal groupoids

2008

If His a G-crossed module, the set of derivations of Gin H is a monoid under the Whitehead product of derivations. We interpret the Whitehead product using the correspondence between crossed modules and internal groupoids in the category of groups. Working in the general context of internal groupoids in a finitely complete category, we relate derivations to holomorphisms, translations, affine transformations, and to the embedding category of a groupoid. (C) 2007 Elsevier B.V. All rights reserved.

Higher-dimensional algebraAlgebra and Number TheoryComplete categoryCategory of groupsContext (language use)derivations crossed modules internal groupoids holomorphismsAlgebraSettore MAT/02 - AlgebraMathematics::K-Theory and HomologyMathematics::Category TheoryMonoid (category theory)EmbeddingAffine transformationMathematics::Symplectic GeometryMathematicsWhitehead productJournal of Pure and Applied Algebra
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