Geodesic
Galois theory and the categorical Peiffer commutator
Homology, homotopy, and applications, Tome 22 (2020) no. 2, pp. 323-346.

Voir la notice de l'article provenant de la source International Press of Boston

We show that the Peiffer commutator previously defined by Cigoli, Mantovani and Metere can be used to characterize central extensions of precrossed modules with respect to the subcategory of crossed modules in any semi-abelian category satisfying an additional property. We prove that this commutator also characterizes double central extensions, obtaining then some Hopf formulas for the second and third homology objects of internal precrossed modules.
DOI : 10.4310/HHA.2020.v22.n2.a20
Classification : 17B55, 18D35, 18G50, 20J05
Keywords: crossed module, Galois theory, Peiffer commutator, central extension, semiabelian category 
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     author = {Alan S. Cigoli and Arnaud Duvieusart and Marino Gran and Sandra Mantovani},
     title = {Galois theory and the categorical {Peiffer} commutator},
     journal = {Homology, homotopy, and applications},
     pages = {323--346},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n2.a20/}
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Alan S. Cigoli; Arnaud Duvieusart; Marino Gran; Sandra Mantovani. Galois theory and the categorical Peiffer commutator. Homology, homotopy, and applications, Tome 22 (2020) no. 2, pp. 323-346. doi : 10.4310/HHA.2020.v22.n2.a20. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n2.a20/

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