Homology, Homotopy and Applications
Volume 12 (2010)
On the second cohomology group of a simplicial group
Pages: 167 – 210
We give an algebraic proof for the result of Eilenberg and Mac Lane that the second cohomology group of a simplicial group G can be computed as a quotient of a fibre product involving the first two homotopy groups and the first Postnikov invariant of G. Our main tool is the theory of crossed module extensions of groups.
cohomology; simplicial groups; crossed modules
2010 Mathematics Subject Classification
18D35, 18G30, 20J06, 55U10