# Artin-Mazur codiagonal preserves Kan objects?

The Artin-Mazur codiagonal $\nabla:ssSet \to sSet$ is right adjoint to the total decalage functor $Dec:sSet \to ssSet$. The total decalage functor is defined to be precomposition with the ordinal sum functor $+:\Delta\times \Delta \to \Delta$, $+([n],[m]) = [n+m+1]$.

If we agree to call a bisimplicial set $X= ([n]\times [m] \mapsto X_{nm})$ a bi-Kan complex if each simplicial set $[k] \mapsto X_{km}$ and $[k] \mapsto X_{nk}$ is a Kan complex (for all $n$ and $m$), then I'm wondering if it is known in the literature whether $\nabla X$ is a Kan complex. Perhaps in Artin-Mazur's monograph?

Note that a bi-Kan complex is not necessarily the same as an internal Kan complex in the category of Kan complexes (I haven't checked this - just a warning)

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For some reason, I think that the only people who can answer this are Tim Porter or Phil Ehlers. –  Harry Gindi Feb 22 '11 at 23:37