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Arguments working entirely at a high level of abstraction, particularly category-theoretic arguments.

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The single-plus construction is not the left adjoint of the inclusion of separated presheaves?

If $(-)^+$ were left adjoint to $\iota$, we would have $(-)^+\circ\iota=id.$, but this is impossible since $(-)^+$ applied to a separated presheaf gives its sheafification.
Kevin Ventullo's user avatar