The monoidal unit of the coproduct of sets is the functor
\[ \mathbb {0}^{\mathsf{Sets}} \colon \mathsf{pt}\to \mathsf{Sets} \]
defined by
\[ \mathbb {0}_{\mathsf{Sets}}\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\text{Ø}, \]
where $\text{Ø}$ is the empty set of Chapter 2: Constructions With Sets, Definition 2.3.1.1.1.
