Exponentiation (Category Theory)

In Monoidal Category, an exponential object of $A$ $B$ written $B^A$ together with a family of morphisms $ex:A\text{texttimes}{B}^A\to B$. Such that $\mathrm{Hom}[A\otimes C,B]\cong \mathrm{Hom}[C,B^A]$ This is also called “Internal Hom”.

Sources

https://ncatlab.org/nlab/show/hom-object