Exponential object

Summary

An exponential object $Z^Y$ in a category with products is an object of morphisms from $Y$ to $Z$, together with an evaluation morphism. It is defined by a universal property that expresses currying: maps $X \times Y \to Z$ match maps $X \to Z^Y$. Exponential objects are the defining feature of Cartesian closed categories. They give the semantics of function types in lambda calculus.