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nLab > Latest Changes: twisted arrow (∞,1)-category

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    • CommentRowNumber1.
    • CommentAuthorHurkyl
    • CommentTimeFeb 25th 2021

    Created an entry for this.

    I’ve adopted the existing convention at nLab in the definition of Tw(C)Tw(C) (which is also the definition I prefer).

    Since the opposite convention is used a lot (e.g. by Lurie), I’ve decided it was worth giving it notation, the relation between the versions, and citing results in both forms. Since I didn’t have any better ideas, I’ve settled on Tw¯(C)\overline{Tw}(C).

    v1, current

    • CommentRowNumber2.
    • CommentAuthorHurkyl
    • CommentTimeMay 28th 2022

    Added link to the Kerodon, and added some citations to it.

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 28th 2022

    added some redirects:

      [[!redirects twisted arrow (∞,1)-categories]]

  [[!redirects twisted arrow (infinity,1)-category]]
  [[!redirects twisted arrow (infinity,1)-categories]]

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorHurkyl
    • CommentTimeMay 28th 2022

    I suppose citations should be to tags rather than proposition numbers. I’ll change it when I can edit the page again.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 28th 2022

    (Thanks for fixing my typo in that link!)

    I find that, in the bulk text, it’s more natural for the reader to refer to proposition numbers instead of tags, since the former is meant for humans to read, the latter more for computers.

    But probably the tags are guaranteed to be stable over time, while the proposition numbers might not be. In general at least. In the case of Kerodon I would still be amazed, but not surprised, if the material emerges all in perfect order right away, like Athena from Zeus’ forehead.

    • CommentRowNumber6.
    • CommentAuthorHurkyl
    • CommentTimeMay 28th 2022

    Included a statement that TwTw, as defined on quasicategories, actually descends to a functor on infinity categories. (and a couple other minor improvements)

    diff, v5, current

    • CommentRowNumber7.
    • CommentAuthorHurkyl
    • CommentTimeApr 2nd 2023

    Something weird is going on with the formatting. \overline{…} is only producing a tiny overline, rather than one spanning the word.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeApr 2nd 2023

    It looks fine on my system. Maybe you could isolate a minimal example in the Sandbox.

    • CommentRowNumber9.
    • CommentAuthorHurkyl
    • CommentTimeJun 6th 2023
    • (edited Jun 6th 2023)

    I forgot to follow up on this. I’ve created an example at Sandbox. On my computer, I only get a one character wide overline (over the “y” in “Tiny”), rather than something spanning the entire text. I’ve tested using both Edge and Opera. As mentioned in my previous comment, this looked fine when I originally created the page, and I think I first noticed it behaving badly around the time I made the comment.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJun 7th 2023

    I see. On my system this comes out fine with Firefox, but broken in the way you describe with Edge and Chrome.

    I’ll raise this point to the technical team now.

    • CommentRowNumber11.
    • CommentAuthorHurkyl
    • CommentTimeMar 12th 2024

    Added a proposition about the behavior under change of category, and a proof that TwTw is a right Quillen functor on quasicategories.

    diff, v6, current

1 to 11 of 11

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