Homology, Homotopy and Applications
Volume 22 (2020)
Galois theory and the categorical Peiffer commutator
Pages: 323 – 346
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.
crossed module, Galois theory, Peiffer commutator, central extension, semiabelian category
2010 Mathematics Subject Classification
17B55, 18D35, 18G50, 20J05
Copyright © 2020, Alan S. Cigoli, Arnaud Duvieusart, Marino Gran and Sandra Mantovani. Permission to copy for private use granted.
The second author is a Research Fellow of the Fonds de la Recherche Scientifique-FNRS.
Received 22 July 2019
Accepted 17 January 2020
Published 13 May 2020