# exponential object

An exponential object generalizes its interpretation in category ${\displaystyle \mathbf {Set} }$; namely, that of as a function set or internal hom-set.
The pair ${\displaystyle Z^{Y},{\mbox{eval}}:Z^{Y}\times Y\rightarrow Z}$ is the terminal object of the comma category ${\displaystyle (-\times Y)\downarrow Z}$. Therefore the exponential object is a kind of universal morphism.