6533b828fe1ef96bd1288437

RESEARCH PRODUCT

Fibred-categorical obstruction theory

Sandra MantovaniAlan S. CigoliEnrico VitaleGiuseppe Metere

subject

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

description

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.

yearjournalcountryeditionlanguage
2022-03-01
10.1016/j.jalgebra.2021.10.040http://hdl.handle.net/10447/525060