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nLab > Latest Changes: geometry of physics -- categories and toposes

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 3rd 2018

    I’ll be preparing here notes for my lectures Categories and Toposes (schreiber), later this month.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 5th 2018

    In Definition 2.14, clause 3, isn’t that monoidal product rather than cartesian product?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 5th 2018
    • (edited Jun 5th 2018)

    Thanks for catching this, fixed now.

    In fact, large parts of text still need to be transferred from TopTop-enrichment to arbitrary 𝒱\mathcal{V}-enrichment.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 13th 2018

    removed the spurious capitalization from the entry title

    diff, v43, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJul 21st 2018

    finally made it to the discussion of “solid model toposes” in the last section (here). This should set the scope. Still need to expand and polish some bits, but maybe not add any further sections.

    • CommentRowNumber6.
    • CommentAuthorAli Caglayan
    • CommentTimeSep 20th 2018
    • (edited Sep 20th 2018)
    Is it normal for this page to take a few minutes to load? I have noticed similar performance issues with the stable homotopy articles too. Would it possible for long nlab articles to have pages? I am on a chromebook using google chrome.

  7. It depends what you mean by load. If you mean that all the MathJax is finished, then yes, it takes forever. If you mean that the page is loaded apart from the MathJax, then no, it is not normal after the rendering changes made a couple of months ago; it takes a while only the very first time it is loaded after an edit (this generates the cache). Eventually the latter will be changed as well, so that the loading is always more or less immediate (apart from MathJax).

  8. Pagination could be an interesting idea, though, for the future.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeSep 20th 2018
    • (edited Sep 20th 2018)

    With Firefox it works pleasantly. Firefox (and its derivatives) is the only browser left that has native MathML support, since all other browsers abondened support for it some years ago. That’s what makes the difference in rendering the maths.

    I keep thinking we should have a general announcement on nnLab pages, that recommends Firefox to the reader.

    And we should pray that the Mozillas never ever decide to remove their MathML support, too.

    • CommentRowNumber10.
    • CommentAuthorRichard Williamson
    • CommentTimeSep 20th 2018
    • (edited Sep 20th 2018)

    I keep thinking we should have a general announcement on nLab pages, that recommends Firefox to the reader.

    Maybe you’re right after all! Maybe others can share their opinion on this; if enough think it a good idea, I will implement it.

    That’s [i.e. MathML is] what makes the difference in rendering the maths.

    I would say that that’s not quite true. What makes MathJax slow is only that it is client side, i.e. done in the user’s browser, it does not have to do with the use of MathML. What we really need, in my opinion, is a good server side way to produce HTML/CSS for mathematics directly, without using MathML. I am making some steps towards this myself, but of course it is a significant undertaking.

    • CommentRowNumber11.
    • CommentAuthorAli Caglayan
    • CommentTimeSep 20th 2018
    I have tried firefox and it seems to be running much faster, the bottleneck seems to be the server response time (which is fine). I have also read that Safari supports mathml and its only chrome that stopped support. They deemed it unsuportted and risky which could include security issues. Luckily for us one of the engineers say that MathJax works just fine for the equations and we should take his word.

    Also on an unrelated note: are my forum posts padded or not? I have tried from another browser and it seems that everybody elses posts are padded but mine.

  12. Hi Ali, your forum posts look the same to me as everyone else’s. Is it possible for you to share a screenshot? Maybe via Dropbox or something, if you use that.

    • CommentRowNumber13.
    • CommentAuthorMike Shulman
    • CommentTimeSep 20th 2018

    Alizter, the reason your forum posts are not “padded” is that you’ve chosen the “Text” markup option rather than the default “Markdown+Itex” option: check the radio buttons underneath the text entry box.

    • CommentRowNumber14.
    • CommentAuthorAli Caglayan
    • CommentTimeSep 20th 2018
    • (edited Sep 20th 2018)
    • CommentRowNumber15.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJan 19th 2020
    The end of proposition 1.66 (the case when C is fully faithful)
    says that CL is left adjoint to CR, which is correct.

    But Lemma 1.68 (the same case of fully faithful C)
    suddenly claims that CR is left adjoint to CL,
    which seems wrong to me.

    This wrong claim is then repeated in several places,
    including Proposition 1.69.
    • CommentRowNumber16.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJan 19th 2020
    And, furthermore, in formula (29), the functor Γ should probably be replaced by R.
    • CommentRowNumber17.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJan 19th 2020
    • (edited Jan 19th 2020)
    And in Definition 1.72 the top left corner should probably be □_2, not □_1. And the 3 occurrences of "box" should probably read □.
    • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeJan 20th 2020

    Thanks for catching typos!

    I have now fixed all the instances that you mentioned explicitly.

    For your “and in several places” I scrolled around a little and didn’t see any further instances right away. I am sure there are, and I can try to hunt them down later.

    • CommentRowNumber19.
    • CommentAuthorGuest
    • CommentTimeJul 19th 2021
    Definition 1.9 has a typo. The inverse should be from Y to X instead of Y to Y.
    • CommentRowNumber20.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 19th 2021

    Thanks. I made the change on the page that was inserted in this one, geometry of physics – basic notions of category theory.

    • CommentRowNumber21.
    • CommentAuthorUrs
    • CommentTimeJul 19th 2021

    Thanks!

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