The skew right unitor of the right tensor product of pointed sets is the natural transformation
\[ \rho ^{\mathsf{Sets}_{*},\rhd }_{X} \colon X\rhd S^{0}\to X \]
at $\webleft (X,x_{0}\webright )\in \text{Obj}\webleft (\mathsf{Sets}_{*}\webright )$ is given by the composition
\begin{align*} X\rhd S^{0} & \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*}
