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.
Fibred-categorical obstruction theory / A.S. Cigoli, S. Mantovani, G. Metere, E.M. Vitale. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 593(2022), pp. 105-141. [10.1016/j.jalgebra.2021.10.040]
Fibred-categorical obstruction theory
S. MantovaniSecondo
;
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.
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