• The characteristic function
    \[ \chi _{x}\colon X\to \{ \mathsf{t},\mathsf{f}\} \]

    of an element $x$ of $X$ is a decategorification of the representable presheaf

    \[ h_{X}\colon \mathcal{C}^{\mathsf{op}} \to \mathsf{Sets} \]

    of an object $x$ of a category $\mathcal{C}$.


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