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

Sources

• 1998: Saunders Mac Lane: Categories for the Working Mathematician (2nd ed.): $\S \text{I}.3$: Functors