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

Lusternik-Schnirelmann category of simplicial complexes and finite spaces