Fibred-categorical obstruction theory

Cigoli, Alan Stefano;Mantovani, Sandra;Metere, Giuseppe;Vitale, Enrico
(2021) Journal of Algebra — Vol. 593, n° np, p. 105-141 (2021)

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Authors
  • Cigoli, Alan Stefanoorcid-logoUCLouvain
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  • Mantovani, Sandra
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  • Metere, Giuseppe
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  • Vitale, Enricoorcid-logoUCLouvain
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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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Cigoli, A. S., Mantovani, S., Metere, G., & Vitale, E. (2021). Fibred-categorical obstruction theory. Journal of Algebra, 593(np), 105-141. https://doi.org/10.1016/j.jalgebra.2021.10.040 (Original work published 2021)