The skew left unitor of the left tensor product of pointed sets is the natural transformation
\[ \lambda ^{\mathsf{Sets}_{*},\lhd }_{X} \colon S^{0}\lhd X \to X \]
at $\webleft (X,x_{0}\webright )\in \text{Obj}\webleft (\mathsf{Sets}_{*}\webright )$ is given by the composition
\begin{align*} S^{0}\lhd X & \cong |X|\odot S^{0}\\ & \cong \bigvee _{x\in X}S^{0}\\ & \rightarrow X, \end{align*}
where $\bigvee _{x\in X}S^{0}\to X$ is the map given by
\begin{align*} \webleft [\webleft (x,0\webright )\webright ] & \mapsto x_{0},\\ \webleft [\webleft (x,1\webright )\webright ] & \mapsto x. \end{align*}
