The monoidal unit of the product of sets is the functor
\[ \mathbb {1}^{\mathsf{Sets}} \colon \mathsf{pt}\to \mathsf{Sets} \]
defined by
\[ \mathbb {1}_{\mathsf{Sets}}\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\mathrm{pt}, \]
where $\mathrm{pt}$ is the terminal set of Chapter 4: Constructions With Sets, Definition 4.1.1.1.1.
