Definition Dual minmax problem [lcc-001J]

Let L = (X,Y,L) be a minmax problem. Then let L^* denote the dual problem given by (Y,X,L^*(y,x) = -L(x,y)).

If \phi = (\phi ^+,\phi ^-) : L \to L' is a morphism of minmax problems, then \phi ^* = (\phi ^-,\phi ^+): L'^* \to L^* is again a morphism in the other direction. This assignment makes (-)^* into a self-inverse functor on the category of minmax problems