Item 2 (0079) — The Clowder Project

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Powersets as Sets of Functions II. The bijection
\[ \mathcal{P}\webleft (X\webright )\cong \mathsf{Sets}\webleft (X,\{ \mathsf{t},\mathsf{f}\} \webright ) \]

of Item 1 is natural in $X\in \text{Obj}\webleft (\mathsf{Sets}\webright )$, refining to a natural isomorphism of functors

\[ \mathcal{P}^{-1}\cong \mathsf{Sets}\webleft (-,\{ \mathsf{t},\mathsf{f}\} \webright ). \]

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