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 / A.S. Cigoli, A. Duvieusart, M. Gran, S. Mantovani. - In: HOMOLOGY, HOMOTOPY AND APPLICATIONS. - ISSN 1532-0073. - 22:2(2020), pp. 323-346. [10.4310/HHA.2020.V22.N2.A20]

Galois theory and the categorical Peiffer commutator

Duvieusart A.;Mantovani S.
2020

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.
Central extension; Crossed module; Galois theory; Peiffer commutator; Semi-abelian category
Settore MAT/02 - Algebra
Settore MAT/04 - Matematiche Complementari
HOMOLOGY, HOMOTOPY AND APPLICATIONS
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/746592
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