  With any locally finite partially ordered set $K$ its incidence algebra
$\Omega(K)$ is associated. We shall consider algebras over fields with
characteristic zero. In this case there is a correspondence $K \leftrightarrow
\Omega(K)$ such that the poset $K$ can be reconstructed from its incidence
algebra up to an isomorphism -- due to Stanley theorem. In the meantime, a
monotone mapping between two posets in general induces no homomorphism of their
incidence algebras.
  In this paper I show that if the class of posets is confined to simplicial
complexes then their incidence algebras acquire the structure of differential
moduli and the correspondence $K\leftrightarrow\Omega(K)$ is a contravariant
functor.
