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