• A function
    \[ f\colon X\to \{ \mathsf{t},\mathsf{f}\} \]

    is a decategorification of a presheaf

    \[ \mathcal{F}\colon \mathcal{C}^{\mathsf{op}}\to \mathsf{Sets}, \]

    with the characteristic functions $\chi _{U}$ of the subsets of $X$ being the primordial examples (and, in fact, all examples) of these.


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