Equivariant-constructible Koszul duality for dual toric varieties

For affine toric varieties X and defined by dual cones, we define an equivalence of categories between mixed versions of the equivariant derived category and the derived category of sheaves on which are locally constant with unipotent monodromy on each orbit. This equivalence satisfies the Koszul duality formalism of Beilinson, Ginzburg, and Soergel.