Search results for "Category of fractions"

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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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