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