The left $J$-skew monoidal unit of $\mathbf{Rel}\webleft (A,B\webright )$ is the functor
\[ \mathbb {1}^{\mathbf{Rel}\webleft (A,B\webright )}_{\lhd _{J}} \colon \mathsf{pt}\to \mathbf{Rel}\webleft (A,B\webright ) \]
picking the object
\[ \mathbb {1}^{\lhd _{J}}_{\mathbf{Rel}\webleft (A,B\webright )}\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}J \]
of $\mathbf{Rel}\webleft (A,B\webright )$.
