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The category of prosets is a coreflective subcategory of the category of topological spaces. I edited in this observation at specialization order, and am removing a query box:
+–{.query} There's an adjunction here; I should think about which way it goes and whether it's a reflection or something. —Toby Mike: If it exists, it’s either a reflection or a coreflection, since the functor $\Pros \to \Top$ is fully faithful. =–
Thanks!
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