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.File | Dimensione | Formato | |
---|---|---|---|
GaloisPeiffer.pdf
accesso aperto |
322.17 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.