In category theory, a branch of mathematics, a power object in a category is an analogue of a powerset in the category of sets.

Definition

be a finitely complete category. A power object together with a subobject satisfying the following universal property.

Properties

In the category of sets is the set membership relation.

More generally, in any elementary topos is the subobject classifier being the subobject classified by the evaluation map.

Conversely, every finitely complete category with power objects is an elementary topos. Thus, power objects provide a possible simplification of the definition of an elementary topos.

Citations

References