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. Fu r t h e r 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.
Cigoli, A., Mantovani, S., Metere, G., Vitale, E. (2022). Fibred-categorical obstruction theory. JOURNAL OF ALGEBRA, 593, 105-141 [10.1016/j.jalgebra.2021.10.040].
Fibred-categorical obstruction theory
Cigoli, A. S.;Metere, G.
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2022-03-01
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. Fu r t h e r 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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Journal of Algebra 593 (2022) 105–141.pdf
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