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