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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 “BB” in the first two instances, to “RR” in following instances.

    I changed it to all “BB“s, assuming that the intention was that the following section uses the same “BB“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,CB,C over AA the type of equivalences between the total types of BB and CC is equivalent to the type of pointwise equivalences between BB and CC. 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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