• Adjointness. We have an adjunction
    witnessed by a bijection of sets
    \begin{align*} \mathsf{Sets}_{*}\webleft (\webleft (X^{+},\star _{X}\webright ),\webleft (Y,y_{0}\webright )\webright )\cong \mathsf{Sets}\webleft (X,Y\webright ),\end{align*}

    natural in $X\in \text{Obj}\webleft (\mathsf{Sets}\webright )$ and $\webleft (Y,y_{0}\webright )\in \text{Obj}\webleft (\mathsf{Sets}_{*}\webright )$.


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