The monoidal unit of the smash product of pointed sets is the functor
\[ \mathbb {1}^{\mathsf{Sets}_{*}} \colon \mathsf{pt}\to \mathsf{Sets}_{*} \]
defined by
\[ \mathbb {1}_{\mathsf{Sets}_{*}}\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}S^{0}. \]
