Search results for "Higher-dimensional algebra"

showing 3 items of 3 documents

Semidirect products of internal groupoids

2010

We give a characterization of those finitely complete categories with initial object and pushouts of split monomorphisms that admit categorical semidirect products. As an application we examine the case of groupoids with fixed set of objects. Further, we extend this to the internal case. (C) 2010 Elsevier B.V. All rights reserved.

Set (abstract data type)AlgebraSettore MAT/02 - AlgebraHigher-dimensional algebraAlgebra and Number Theorysemi-direct product groupoid internal structuresMathematics::Category TheoryCharacterization (mathematics)Categorical variableInitial and terminal objectsMathematicsJournal of Pure and Applied Algebra
researchProduct

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
researchProduct

On spectra of geometric operators on open manifolds and differentiable groupoids

2001

We use a pseudodifferential calculus on differentiable groupoids to obtain new analytical results on geometric operators on certain noncompact Riemannian manifolds. The first step is to establish that the geometric operators belong to a pseudodifferential calculus on an associated differentiable groupoid. This then leads to Fredholmness criteria for geometric operators on suitable noncompact manifolds, as well as to an inductive procedure to compute their essential spectra. As an application, we answer a question of Melrose on the essential spectrum of the Laplace operator on manifolds with multicylindrical ends.

Discrete mathematicsPure mathematicsHigher-dimensional algebraMathematics::Operator AlgebrasGeneral MathematicsEssential spectrumMathematics::Spectral TheoryOperator theoryCompact operatorQuasinormal operatorMathematics::K-Theory and HomologyDouble groupoidMathematics::Differential GeometryDifferentiable functionMathematics::Symplectic GeometryLaplace operatorMathematicsElectronic Research Announcements of the American Mathematical Society
researchProduct