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nLab > Latest Changes: first-order hyperdoctrine

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  1. adding link to geometric hyperdoctrine

    Anonymous

    diff, v17, current

    • CommentRowNumber2.
    • CommentAuthormaxsnew
    • CommentTimeJun 15th 2023

    An alternative formulation of first-order hyperdoctrines in terms of the internal language of presheaf categories. No known citation, I just realized it recently when I was working with them. Has anyone seen it before?

    diff, v19, current

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 15th 2023

    I don’t think I’ve seen it. But I’m fuzzy on property 1. Why isn’t this automatic from the fact that PP already carries an internal Heyting algebra structure?

    • CommentRowNumber4.
    • CommentAuthormaxsnew
    • CommentTimeJun 15th 2023

    Being an internal Heyting algebra means it has internal finite meets and joins, i.e., nullary and binary, and representables are tiny but they aren’t finite. The representable-indexed meets and joins give you universal and existential quantifiers respectively.

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 16th 2023

    Thanks. I don’t think I’ve heard the expression “representable-indexed meets and joins”.

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