Power Object

Let $\mathcal{V}$ be a Closed Monoidal Category and $\mathcal{C}$ be a $\mathcal{V}$ -Enriched Category. The power of an object $c:\mathcal{C}$ by an object $v:\mathcal{V}$ is an object $\pitchfork(v,c):C$ along with a Natural Isomorphism

${{-}\to{\pitchfork(v,c)}}\cong{{v}\to{{{-}\to{c}}}}$

Examples

Power objects in Category of Sets are set-indexed Cartesian Products of the same object; EG:

$\pitchfork(I,X)=\prod_{s\in S}X$

References

https://ncatlab.org/nlab/show/powering