Abstract
We introduce for a crossed module (T,G,∂) an invariant H 2 q(T,G,∂) (q being a nonnegative integer) that generalizes the second Eilenberg–MacLane homology group with coefficients in Z q . We give for a q-perfect crossed module, the universal q-central extension via the non-abelian tensor product modulo q of two crossed modules, whose kernel is the mentioned invariant.
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Grandjeán, A.R., López, M.P. H 2 q(T,G,∂) and q-perfect Crossed Modules. Applied Categorical Structures 11, 171–184 (2003). https://doi.org/10.1023/A:1023507229607
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DOI: https://doi.org/10.1023/A:1023507229607