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nLab > Latest Changes: principle of unique choice

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    • CommentRowNumber1.
    • CommentAuthormaxsnew
    • CommentTimeAug 7th 2022

    Init this page, which is referenced quite a few times. I’m not much of an expert on these weak foundations so if someone else would like to fill in some details that would be nice.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorjonsterling
    • CommentTimeAug 7th 2022

    Thanks for starting this. It would be really great to use this page to clarify a lot of misconceptions. For instance, it is sometimes said that unique choice holds in any lex category — I think there is a sense in which this is true, but it is not at all the pertinent sense.

    • CommentRowNumber3.
    • CommentAuthormaxsnew
    • CommentTimeSep 2nd 2022

    Discuss the relationship to adjunctions in Rel and how adjunctions in Prof do not satisfy the analogous property.

    I guess the analogous statement for preorders needs a form of choice (and doesn’t if they are posets). What about groupoids?

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorGuest
    • CommentTimeSep 2nd 2022

    this mathoverflow question might be useful

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeSep 3rd 2022

    Renamed to “principle of unique choice”

    diff, v3, current

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeSep 3rd 2022

    A quasitopos has (at least) two “internal languages”, one that satisfies unique choice and one that doesn’t.

    I’m curious what you had in mind about lex categories, Jon. It does seem to me that the most obvious formulation of unique choice in an arbitrary lex category is the one using arbitrary subobjects, and that one holds.

    diff, v3, current

  7. added a section on the principle of unique choice in type theory

    Anonymous

    diff, v4, current

    • CommentRowNumber8.
    • CommentAuthormaxsnew
    • CommentTimeFeb 27th 2024

    redirect “function comprehension principle”

    diff, v9, current

1 to 8 of 8

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