Type duality and polynomial functors

[ncfavier]

Type duality talks about a natural transformation between a covariant functor and a contravariant one, which doesn't make sense. We are really talking about the contravariant functor that has the same object mapping as the polynomial endofunctor of the universe but whose action on morphisms is given by pullback. Maybe this should be clarified.

[fredrik-bakke]

Assigning and pinging the author, @EgbertRijke.