I am not familiar with the Artin-Mazur codiagonal, but Jon Beck once showed me a proof (unpublished like most of his work) that the geometric realization of the diagonal and of the whole thing were homotopic. The geometric realization of the whole thing was a coend of X_{ij} x \Delta_i x \Delta_j. The proof of the homology is much easier and will appear in my forthcoming Acyclic Models. On Thu, 4 Apr 2002, Prof. T.Porter wrote:

Dear all,

It is folklore that for a bisimplicial group $X_{*,*}$ the diagonal and the Artin Mazur `codiagonal' construction have the same homotopy type.

Can anyone point me to a published proof?

Thanks,

Tim Porter