The right $J$-skew right unitor of $\mathbf{Rel}(A,B)$ is the natural transformation
\[ \rho ^{\mathbf{Rel}(A,B),\rhd _{J}} \colon {\rhd _{J}}\circ {(\mathsf{id}\times \mathbb {1}^{\mathbf{Rel}(A,B)}_{\rhd })} \Longrightarrow \mathbf{\rho }^{\mathsf{Cats}_{\mathsf{2}}}_{\mathbf{Rel}(A,B)}, \]
as in the diagram
\[ \rho ^{\mathbf{Rel}(A,B),\rhd _{J}}_{S}\colon \underbrace{S\rhd _{J}J}_{\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\operatorname {\mathrm{Ran}}_{J}(S)\mathbin {\diamond }J}\hookrightarrow S \]
at $S$ is given by
\[ \rho ^{\mathbf{Rel}(A,B),\rhd _{J}}_{S}\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\epsilon _{R}, \]
where $\epsilon \colon J^{*}\circ \operatorname {\mathrm{Ran}}_{J}\Longrightarrow \operatorname {\mathrm{id}}_{\mathbf{Rel}(A,B)}$ is the counit of the adjunction $J^{*}\dashv \operatorname {\mathrm{Ran}}_{J}$.
