Theorem: Let ${}\in\mathcal{S}\mathrm{et}$ be the terminal object in $\mathcal{S}\mathrm{et}$.Then $\hom_{\mathcal{S}\mathrm{et}}({},-):\mathcal{S}\mathrm{et}\to\mathcal{S}\mathrm{et}$ is an equivalence of categories.
Theorem: Let ${}\in\mathcal{S}\mathrm{et}$ be the terminal object in $\mathcal{S}\mathrm{et}$.Then $\hom_{\mathcal{S}\mathrm{et}}({},-):\mathcal{S}\mathrm{et}\to\mathcal{S}\mathrm{et}$ is an equivalence of categories.