D. Conduch

Simplicial Crossed Modules and Mapping Cones

abstract:
Given a bisimplicial group $G_{\star \star } $ such that $N(G)_{\star q} = \{ 1 \} $ for $q \geq 2$, a simplicial group is obtained whose Moore complex is a mapping cone of the chain morphism $N(G)_{\star 1} \to N(G)_{\star 0} $. This simplicial group is homotopy equivalent to the diagonal of $G_{\star \star} $. In the last section a special case is considered.