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arXiv · 0911.2864

On the second cohomology group of a simplicial group

Sebastian Thomas
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Abstract

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.

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Sebastian Thomas. 2009-11-15. On the second cohomology group of a simplicial group. https://arxiv.org/abs/0911.2864

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