The skew right unitor of the left tensor product of pointed sets is the natural transformation
\[ \rho ^{\mathsf{Sets}_{*},\lhd }_{X} \colon X \to X\lhd S^{0} \]
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 X\lhd S^{0}, \end{align*}
where $X\to X\vee X$ is the map sending $X$ to the second factor of $X$ in $X\vee X$.
