Power object
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In category theory, a branch of mathematics, a power object in a category is an analogue of a powerset in the category of sets.
In category theory, a branch of mathematics, a power object in a category is an analogue of a powerset in the category of sets. More generally, in any elementary topos, the power object of A can be constructed as \mathcal{P}(A) := \Omega^A (where \Omega is the subobject classifier), with (\in) \hookrightarrow A \times \Omega^A being the subobject classified by the evaluation map A \times \Omega^A \to \Omega . 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.
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