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

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

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

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

    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.

    diff, v17, current

    • CommentRowNumber4.
    • CommentAuthorHurkyl
    • CommentTimeOct 22nd 2020

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

    diff, v18, current

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