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

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