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 $\mathbf{Rel}\webleft (A,B\webright )$.


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