Definition:Contravariant Power Set Functor

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

The contravariant power set functor $\overline{\mathcal P} : \mathbf{Set} \to \mathbf{Set}$ is the covariant functor which sends:
 * An object $x$ to its power set $\mathcal P(x)$.
 * A morphism $f : x \to y$ to the inverse image mapping $\overline{\mathcal P}(f) : \mathcal P(y) \to \mathcal P(x)$.

Also see

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