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

Sources

• 1998: Saunders Mac Lane: Categories for the Working Mathematician (2nd ed.): $\S \text{II}.2$: Contravariance and Opposites