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nLab: 2-functors

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    • CommentRowNumber1.
    • CommentAuthorAlec Rhea
    • CommentTimeFeb 25th 2019
    • (edited Feb 25th 2019)
    It seems like the pages 2-functor, strict 2-functor and pseudofunctor could all be smoothly merged into one '2-morphism' page, perhaps beginning with the most relaxed version of a 2-morphism between 2-categories (maybe even lax functors) and then gradually strictifying to produce the restricted versions, culminating with a strict 2-functor.

    At the very least the pages all curently feel circular when trying to learn what exactly a 2-functor is, with pseudofunctor the only page really providing any accessible definitions (but they are very nice and explicit).

    I have the various definitions and diagrams latexed up in my own notes (using xypic syntax) and would copy-paste them in and rewrite/merge the pages myself (assuming there are no objections) but I'm not sure which levers to pull on the nLab to merge/delete pages, or if a lowly browser like me even has such powers.
    • CommentRowNumber2.
    • CommentAuthorRichard Williamson
    • CommentTimeFeb 25th 2019
    • (edited Feb 25th 2019)

    Hi Alec, we can handle the cleaning up of pages. I suggest that you make a new page, say 2-functor–proposed, where you can put what you like, and get some feedback. Once we’re all agreed, we can handle the old pages.

    I’d be interested to know how the tex to nLab conversion goes. We do have LaTeX section and theorem environments. Let me know if you miss something particularly.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeFeb 25th 2019

    Hmm, I’m not sure I agree with this. I think it’s useful to have separate pages for the three concepts. In particular, when I link to pseudofunctor or strict 2-functor, I want the reader to be taken to a page that is specifically about that concept, rather than a page that’s about a more general concept so that they have to dig through it to find out about the term they clicked on. If the exposition is poor on one or another of those pages, then let’s improve it directly; we can in particular certainly copy and paste from one to another.

    Also a 2-morphism is something quite different! (-:

    • CommentRowNumber4.
    • CommentAuthorRichard Williamson
    • CommentTimeFeb 25th 2019
    • (edited Feb 25th 2019)

    Yes, I definitely agree with Mike that we do probably wish to have all three pages. But I also agree with Alec that it looks like some reorganisation and additions could be very helpful. Maybe Alec can try how he’d like it to look on a new page, and we can then incorporate onto the old pages as people wish; after that, I can manually delete the temporary new page. But also probably you could just try expanding 2-functor, Alec.

    • CommentRowNumber5.
    • CommentAuthorAlec Rhea
    • CommentTimeFeb 25th 2019
    Excellent suggestion Richard, and thank you for the feedback Mike -- I'll edit the sandbox with a potential new version of the 2-functor page, please feel free to offer input/correct mistakes as desired (I am learning this stuff myself at the moment for categorical (non-Galoisian) Galois theory).
    • CommentRowNumber6.
    • CommentAuthorAlec Rhea
    • CommentTimeFeb 25th 2019
    • (edited Feb 25th 2019)
    I've added a section to the bottom of the Sandbox reflecting the presentation I had in mind -- it's currently just a reformulation of pseudofunctors as that's what I had in my notes (and all I had patience for at the moment), but I'll add a section above this for lax functors and a section below it for strict 2-functors which reference the existing diagrams some time tonight if everyone is alright with the layout, and can add the diagrams with some modified text to the lax functor/strict 2-functor page.
    • CommentRowNumber7.
    • CommentAuthorzskoda
    • CommentTimeFeb 26th 2019

    I also think that it is better to have separate pages, as in future more and more specific theorems for each case and formalism will be added and the page would be too difficult to navigate with all versions simulteneously.

    • CommentRowNumber8.
    • CommentAuthorAlec Rhea
    • CommentTimeFeb 26th 2019
    Good call, that hadn't occurred to me and is a very good reason to keep separate pages for each notion. I had envisioned basic definitions and informal discussion of each notion which I think would fit well on the 2-functor page, and each separate page can host the more subtle/deeper theorems about each type of 2-functor as you suggest.

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