Proposition [lcc-001X]

Let L be a minmax problem. Suppose there exists \phi : I \to L \otimes L^*. Then strong duality holds, i.e (L^+)^- \cong (L^-)^+

((\phi )^+)^- gives a morphism I = (I^+)^- \to ((L \otimes L^*)^+)^- \cong (L^+)^- \otimes ((L^*)^+)^- \cong (L^+)^- \otimes ((L^-)^+)^* Here we use the isomorphisms (L^+)^* = (L^*)^- and vice versa, as well as strong monoidality of (-)^- and (-)^+. The existence of that morphism means that (L^+)^- \leq (L^-)^+, which is the other direction of the morphism we wanted.