Duality Functor

Consider the dimensional supermanifold . We will slightly change the notations and instead of denote the coordinates as follows:

Moreover, once we changed the notations for coordinates, we will also rename the supermanifold itself:

The duality functor is an autofunctor on the category of -dimensional supermanifolds. To every supermanifold it associates a dual supermanifold which is the moduli space of -dimensional submanifolds in . We will denote it :