A 2-form between two sup-lattices L and R is defined to be a suplattice bimorphism L×R → 2. Such 2-forms are equivalent to Galois connections, and we study them and their relation to quantales, involutive quantales and quantale modules. As examples we describe applications to C*-algebras.

We construct a 12-uniform hypergraph on n vertices with size (n/12) which satisfies |F ∩ F ′| ∈ {0, 1, 2, 3, 4, 6} for all distinct edges F and F ′.