Definition:Contravariant Power Set Functor

Definition
Let $\mathbf{Set}$ be the category of sets.

The contravariant power set functor $\overline \PP: \mathbf{Set} \to \mathbf{Set}$ is the contravariant functor which sends:
 * An object $x$ to its power set $\powerset x$.
 * A morphism $f : x \to y$ to the inverse image mapping $\map {\overline \PP} f : \powerset y \to \powerset x$.

Also see

 * Contravariant Power Set Functor is Functor
 * Definition:Covariant Power Set Functor