  We describe a procedure to attach a nilpotent strong homotopy Lie algebra to
every simple hypergraph and prove that two hypergraphs are isomorphic if and
only if the corresponding strong homotopy Lie algebras are isomorphic. As an
application, we characterize hypergraphs admitting a system of distinct
representatives in terms of symplectic forms on the corresponding strong
homotopy Lie algebra. We conclude with a combinatorial description of the
cohomology of these strong homotopy Lie algebras in low degree.
