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nLab > Latest Changes: Xena project

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 20th 2019

    Page created, but author did not leave any comments.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 20th 2019

    judging by the latest status report (here) they are making considerable progress with the Xena project, so let’s have a page to record stuff

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 2nd 2019

    Buzzard’s recent post on canonical isomorphism is interesting. I haven’t been following the Xena project. Am I right in thinking they are using Lean but not HoTT? If so, do people think HoTT can treat this canonicity issue properly?

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 2nd 2019

    They are essentially doing classical mathematics in Lean. Certainly not HoTT.

    • CommentRowNumber5.
    • CommentAuthoratmacen
    • CommentTimeJun 2nd 2019

    Mike Shulman had the idea (scroll to the end of the original post for the section “Postscript: which equalities can be made judgmental?”) that HoTT’s judgmental equality could be interpreted as a fully coherent system of paths. So maybe then, the canonical equivalences are the ones that are judgmentally equal to the identity. This way, you formally, absolutely cannot possibly get into trouble thinking of canonical equivalences as equality.

    AFAIK though, it’s not known whether this interpretation actually works.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJun 26th 2019

    added pointer to

    • Kevin Buzzard, The future of Mathematics?, public lecture at the 80th anniversary celebration of CNRS, May 2019 (recording)

    diff, v6, current

1 to 6 of 6

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