Search results for "Schreier-mac lane theorem"

showing 2 items of 2 documents

Fibred-categorical obstruction theory

2022

Abstract We set up a fibred categorical theory of obstruction and classification of morphisms that specialises to the one of monoidal functors between categorical groups and also to the Schreier-Mac Lane theory of group extensions. Further applications are provided to crossed extensions and crossed bimodule butterflies, with in particular a classification of non-abelian extensions of unital associative algebras in terms of Hochschild cohomology.

Pure mathematicsFibrationCohomology Fibration Category of fractions Schreier-Mac Lane theorem Obstruction theory Crossed extension Hochschild cohomologyFibered knotMathematics::Algebraic TopologyCohomologyHochschild cohomologyMorphismMathematics::K-Theory and HomologyMathematics::Category TheoryCategorical variableMathematicsSchreier-Mac Lane theoremAlgebra and Number TheoryFunctorCategory of fractionsGroup (mathematics)Crossed extensionSettore MAT/01 - Logica MatematicaObstruction theoryCohomologyCategory of fractions; Cohomology; Crossed extension; Fibration; Hochschild cohomology; Obstruction theory; Schreier-Mac Lane theoremSettore MAT/02 - AlgebraBimoduleObstruction theory
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Extension theory and the calculus of butterflies

2016

Abstract This paper provides a unified treatment of two distinct viewpoints concerning the classification of group extensions: the first uses weak monoidal functors, the second classifies extensions by means of suitable H 2 -actions. We develop our theory formally, by making explicit a connection between (non-abelian) G-torsors and fibrations. Then we apply our general framework to the classification of extensions in a semi-abelian context, by means of butterflies [1] between internal crossed modules. As a main result, we get an internal version of Dedecker's theorem on the classification of extensions of a group by a crossed module. In the semi-abelian context, Bourn's intrinsic Schreier–M…

TorsorCrossed moduleContext (language use)01 natural sciencesCohomologyCohomology; Extension; Fibrations; Obstruction theory; Schreier-mac lane theorem; TorsorsExtensionMathematics::Category Theory0103 physical sciences0101 mathematicsConnection (algebraic framework)MathematicsAlgebra and Number TheoryFunctorGroup (mathematics)010102 general mathematicsTorsorsExtension (predicate logic)Obstruction theorySchreier-mac lane theoremCohomologyFibrationsAlgebraSettore MAT/02 - AlgebraSchreier–Mac Lane theoremSettore MAT/03 - Geometria010307 mathematical physicsObstruction theory
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