  In this paper we establish a natural definition of Lusternik-Schnirelmann
category for simplicial complexes via the well known notion of contiguity. This
category has the property of being homotopy invariant under strong
equivalences, and only depends on the simplicial structure rather than its
geometric realization.
  In a similar way to the classical case, we also develop a notion of geometric
category for simplicial complexes. We prove that the maximum value over the
homotopy class of a given complex is attained in the core of the complex.
  Finally, by means of well known relations between simplicial complexes and
posets, specific new results for the topological notion of category are
obtained in the setting of finite topological spaces.
