Example 7.7.3.2. Let $X$ and $Y$ be sets, and let $M = \operatorname{Hom}_{\operatorname{Set}}( X, Y )$ denote the set of functions from $X$ to $Y$. Then the evaluation map
\[ \operatorname{ev}: M \times X \rightarrow Y \quad \quad (f,x) \mapsto f(x) \]
exhibits $M$ as an exponential of $Y$ by $X$ in the category of sets. In particular, the category of sets is cartesian closed.