Item 3 (007A) — The Clowder Project

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Powersets as Sets of Relations. We have bijections
\begin{align*} \mathcal{P}\webleft (X\webright ) & \cong \mathrm{Rel}\webleft (\text{pt},X\webright ),\\ \mathcal{P}\webleft (X\webright ) & \cong \mathrm{Rel}\webleft (X,\text{pt}\webright ), \end{align*}

natural in $X\in \text{Obj}\webleft (\mathsf{Sets}\webright )$.

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