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Given a bisimplicial group 𝐺∗∗ such that 𝑁(𝐺)∗ 𝑞 = {1} for 𝑞 ⩾ 2, a simplicial group is obtained whose Moore complex is a mapping cone of the chain morphism 𝑁(𝐺)∗ 1 → 𝑁(𝐺)∗ 0 . This simplicial group is homotopy equivalent to the diagonal of 𝐺∗∗. In the last section a special case is considered.
Georgian Mathematical Journal – de Gruyter
Published: Dec 1, 2003
Keywords: Simplicial group; crossed module; mapping cone; generalized semi-direct product
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