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