• Functionality I. The assignment $f\mapsto f_{!}$ defines a function
    \[ \webleft (-\webright )_{!|A,B}\colon \mathsf{Sets}\webleft (A,B\webright ) \to \mathsf{Sets}\webleft (\mathcal{P}\webleft (A\webright ),\mathcal{P}\webleft (B\webright )\webright ). \]

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