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nLab > Latest Changes: fundamental theorem of identity types

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  1. starting page on the fundamental theorem of identity types

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 12th 2023

    I think there was a typo in that the section With identity induction switched from using “B” in the first two instances, to “R” in following instances.

    I changed it to all “B“s, assuming that the intention was that the following section uses the same “B“s.

    But I am on my phone which makes it hard to harmonize larger chunks of text. Please have a look and double-check.

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorjonsterling
    • CommentTimeDec 19th 2023
    • (edited Dec 19th 2023)

    The claim in the proof that conditions (1-2) are equivalent cannot be true as-stated — namely that for any two families B,C over A the type of equivalences between the total types of B and C is equivalent to the type of pointwise equivalences between B and C. Indeed, one needs in the former case that the equivalences commute with the first projection.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeDec 20th 2023

    I was thinking to clear this entry (by the notorious Anonymous user) until somebody has the energy to fix it, but for the moment I have just added a warning line to the top.

    diff, v6, current

  5. fixed proof that 1 implies 2

    Anonymouse

    diff, v7, current

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