We show that the Peiffer commutator previously defined by Cigoli, Mantovani and Metere can be used to characterize cen-tral extensions of precrossed modules with respect to the sub-category of crossed modules in any semi-abelian category sat-isfying an additional property. We prove that this commuta-tor also characterizes double central extensions, obtaining then some Hopf formulas for the second and third homology objects of internal precrossed modules.
Galois theory and the categorical peiffer commutator
Cigoli A. S.;
2020-01-01
Abstract
We show that the Peiffer commutator previously defined by Cigoli, Mantovani and Metere can be used to characterize cen-tral extensions of precrossed modules with respect to the sub-category of crossed modules in any semi-abelian category sat-isfying an additional property. We prove that this commuta-tor also characterizes double central extensions, obtaining then some Hopf formulas for the second and third homology objects of internal precrossed modules.
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