  We consider a category whose morphisms are bordisms of $n$-dimensional
pseudomanifolds equipped with a certain additional structure (coloring). On the
other hand, we consider the product $G$ of $(n+1)$ copies of infinite symmetric
group. We show that unitary representations of $G$ produce functors from the
category of $(n-1)$-dimensional bordisms to the category of Hilbert spaces and
bounded linear operators.
