Galois theory and the categorical Peiffer commutator
Category Theory
2021-04-13 v1 Algebraic Topology
K-Theory and Homology
Rings and Algebras
Abstract
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.
Keywords
Cite
@article{arxiv.1907.09216,
title = {Galois theory and the categorical Peiffer commutator},
author = {Alan S. Cigoli and Arnaud Duvieusart and Marino Gran and Sandra Mantovani},
journal= {arXiv preprint arXiv:1907.09216},
year = {2021}
}
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29 pages