Weyl-Minkowski duality for integral monoids

The abstract linear duality model of Carvalho and Trotter is extended to accommodate a duality relation shared by point sets and families of (possibly) nonlinear functions. Elementary properties of the general model are established along with results linking finiteness conditions which correspond to well-known (linear) relations of Weyl, Farkas, Minkowski, Lehman and Fulkerson. The particular instance of integer programming duality serves as the main motivation for the general model; duality between finitely generated integral monoids and finite families of Chvátal functions is established in direct analogy to the classical Weyl-Minkowski duality of finitely generated and polyhedral cones. Affine versions of the integral monoid duality results are developed, i.e., duality relations for the integral elements of rational polyhedra.