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nLab > Latest Changes: arity space

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  1.  
    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeJul 24th 2019

    Page created, but author did not leave any comments.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeJul 24th 2019

    Just kind of messing around here, but this seems like a natural common generalization of coherence spaces and finiteness spaces.

    v1, current

    • CommentRowNumber3.
    • CommentAuthorSam Staton
    • CommentTimeJul 25th 2019
    • (edited Jul 25th 2019)

    Nice. I think Girard-Loader totality spaces are κ={1}\kappa=\{1\}, right?

    Also, I thought these kinds of spaces will be always be *-autonomous because they’re built by double-gluing-along-hom-functors + orthogonality, right? (Section 5 of Glueing and orthogonality for models of linear logic, Hyland + Schalk, doi).

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeJul 25th 2019

    Thanks for the pointer! Yes, it looks like totality spaces are unary spaces, except that totality spaces (in the reference I found) include the additional assumption that every element is contained in some unary subset and also some co-unary subset.

    Regarding double gluing and orthogonality, maybe, I’m not familiar with that and don’t have the time to understand it right now. Feel free to add to the entry!

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeJul 25th 2019

    Added mention of totality spaces.

    diff, v2, current

    • CommentRowNumber6.
    • CommentAuthorSam Staton
    • CommentTimeJul 26th 2019

    A bit about generalizing to focuses in categories. It’s not much of a generalization and may be the best setting for this.

    diff, v3, current

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeJul 28th 2019

    Thanks! Maybe it would be better to have a separate page all about this kind of orthogonality, with interlinks?

    • CommentRowNumber8.
    • CommentAuthorSam Staton
    • CommentTimeJul 29th 2019

    link to double gluing

    diff, v4, current

    • CommentRowNumber9.
    • CommentAuthorSam Staton
    • CommentTimeJul 29th 2019

    moved text to double glueing page

    diff, v5, current

    • CommentRowNumber10.
    • CommentAuthormaxsnew
    • CommentTimeAug 18th 2022

    Sketch of the construction of arity spaces based on an orthogonality based on a comment. Maybe @Mike Shulman can see if it’s what he had in mind?

    diff, v6, current

1 to 10 of 10

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