Homology, Homotopy and Applications
Volume 2 (2000)
More about homological properties of precrossed modules
Pages: 105 – 114
Homology groups modulo $q$ of a precrossed $P$-module in any dimensions are defined in terms of nonabelian derived functors, where $q$ is a nonnegative integer. The Hopf formula is proved for the second homology group modulo $q$ of a precrossed $P$-module which shows that for $q=0$ our definition is a natural extension of Conduché and Ellis’ definition [CE]. Some other properties of homologies of precrossed $P$-modules are investigated.
precrossed module, Peiffer abelianization, homology group, nonabelian derived functor
2010 Mathematics Subject Classification
18G10, 18G50, 20J05