Definition:Covariant Power Set Functor

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

The (covariant) power set functor $\PP: \mathbf{Set} \to \mathbf{Set}$ is the covariant functor which sends:
 * An object $x$ to its power set $\powerset x$.
 * A morphism $f: x \to y$ to the direct image mapping $\powerset f: \powerset x \to \powerset y$.

Also see

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