  We look at strict $n$-groupoids and show that if $\Re$ is any realization
functor from the category of strict $n$-groupoids to the category of spaces
satisfying a minimal property of compatibility with homotopy groups, then there
is no strict $n$-groupoid $G$ such that $\Re (G)$ is the $n$-type of $S^2$ (for
$n\geq 3$). At the end we speculate on how one might fix this problem by
introducing a notion of ``snucategory'', a strictly associative $n$-category
with only weak units.
