Extension theory and the calculus of butterflies
(2016) Journal of Algebra —
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- Authors
Cigoli, Alan Stefano 
- Abstract
- This paper provides a unified treatment of two distinct viewpoints concerning the classification of group extensions: the first uses weak monoidal functors, the second classifies extensions by means of suitable H2-actions. We develop our theory formally, by making explicit a connection between (non-abelian) G-torsors and fibrations. Then we apply our general framework to the classification of extensions in a semi-abelian context, by means of butterflies [1] between internal crossed modules. As a main result, we get an internal version of Dedecker's theorem on the classification of extensions of a group by a crossed module. In the semi-abelian context, Bourn's intrinsic Schreier-Mac Lane extension theorem [13] turns out to be an instance of our Theorem 6.3. Actually, even just in the case of groups, our approach reveals a result slightly more general than classical Schreier-Mac Lane theorem.
- Affiliations
Università degli Studi di Milano Dipartimento di Matematica
Citations
Cigoli, A. S., & Metere, G. (2016). Extension theory and the calculus of butterflies. Journal of Algebra. https://doi.org/10.1016/j.jalgebra.2016.03.015