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I have briefly recorded the equivalence of FinSet with finite Booplean algebras at FinSet – Properties – Opposite category. Then I linked to this from various related entries, such as finite set, power set, Stone duality, opposite category.
(I thought we long had that information on the Lab, but it seems we didn’t)
Added to FinSet a remark on the opposite category from a constructive perspective:
“In constructive mathematics, for any flavor of finite, defines an equivalence of with the opposite category of that of those complete atomic Heyting algebras whose set of atomic elements is finite (in the same sense as in the definition of ).”
I don’t know whether for some values of finite, this characterization can be made more interesting, i.e. whether we can give a condition which does not explicitly mention the set of atomic elements.
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