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