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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJan 23rd 2013
• (edited Jan 23rd 2013)

I have briefly recorded the equivalence of FinSet${}^{op}$ 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 $n$Lab, but it seems we didn’t)

1. Added to FinSet a remark on the opposite category $FinSet^{op}$ from a constructive perspective:

“In constructive mathematics, for any flavor of finite, $\mathcal{P}$ defines an equivalence of $FinSet$ 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 $FinSet$).”

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.

• CommentRowNumber3.
• CommentAuthorJohn Baez
• CommentTimeOct 22nd 2020

Added facts about the universal properties of FinSet and its opposite.

• CommentRowNumber4.
• CommentAuthorHurkyl
• CommentTimeOct 22nd 2020

Typo fix: $FinSet^op$ is freely generated by finite limits (not finite colimits).

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