Rockafellar's Theorem on Cyclically Monotone Sets is a result from the foundations of optimal transport. For mathematical objects be a nonempty cyclically monotone set; that is, for every integer mathematical objects and every finite family mathematical objects, with mathematical objects, one has i=0m pi (xi+1 - x. It helps organize the relationship between Monge maps, Kantorovich plans, duality, and Wasserstein geometry.