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nLab > Latest Changes: triangle identities

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  1.  
    • CommentRowNumber1.
    • CommentAuthorTim_Porter
    • CommentTimeJun 8th 2014
    • (edited Jun 8th 2014)

    Someone anonymous has noted that the labels in two diagrams in triangle identities are misplaced. This seems clear. As the diagrams are external, can someone edit them who has access to the original code? There seem to be other errors (e.g. a C should be a D), as well.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 17th 2018

    added a reference pointer to page and verse in Borceux 94

    diff, v17, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 24th 2018
    • (edited Jun 24th 2018)

    In the section As diagrams I slightly re-arranged the text and spacting around the existing svg graphics.

    Then, below that, I included an alternative xymatrix-rendering of the diagrams.

    diff, v18, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 24th 2018

    streamlined and expanded the paragraph Statement. In particular I made sure that the previously missing (!) pointers to adjoint functor and adjunction are included, … and I fixed “natural isomorphism” to “natural transformation” :-/

    diff, v18, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 24th 2018

    also slightly expanded the paragraph in the Idea-section

    diff, v18, current

    • CommentRowNumber6.
    • CommentAuthorKeith Harbaugh
    • CommentTimeMay 20th 2019
    Using Chrome Version 74.0.3729.157 (Official Build) (64-bit) (freshly downloaded on 2019-05-20),
    in the section "As diagrams", get the next three lines of this post:

    As diagrams in the ambient 2-category, the triangle identities look as follows
    Unexpected text node: ' '
    or, equivalently, like so:

    The "Unexpected text node: ' ' " is in a red font inside a yellow box.

    Checking the page source, it looks like this page is using MathJax 2.7.1.
    That was a buggy release, the current release, 2.7.5, has been out since July 2018. It looks stable and more bug free.
    Maybe that's the problem?

  7. I would suggest simply to redo the diagrams in Tikz.

    • CommentRowNumber8.
    • CommentAuthorKeith Harbaugh
    • CommentTimeMay 30th 2019
    Davide Cervone, a MathJax maven, has kindly provided an analysis of what is wrong with this page.
    https://groups.google.com/d/msgid/mathjax-users/8ce162bc-94a8-4371-8969-b8d317ee580a%40googlegroups.com

    In particular, he wrote:

    The error will not go away with version 2.7.5. It is due to the MathML that is in the page, which is not valid. In particular, it contains elements like

    <semantics><annotation-xml encoding="SVG1.1">
    !include adjunction &gt; zigzageta
    </annotation-xml></semantics>

    which look like some preprocessing has failed to be performed. The "!include ..." looks like it is supposed to have been replaced by some SVG, but that hasn't been done. The <annotation-xml> element is supposed to contain XML tags (in this case, SVG tags according to the encoding), but instead contains just a text string, MathJax is complaining about that. Switching versions of mathJax won't help, because the MathML itself is in error, not MathJax's processing of it, in this case.

    My [Keith's] comment: What a helpful person! Thanks very much!

  9. Tried to fix display problem in a diagram

    Baptiste Loreau

    diff, v25, current

  10. Went back to previous version of the diagram to the expense of less clean markup, maybe, so the diagram can merely appear.

    Baptiste Loreau

    diff, v25, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeDec 30th 2020
    • (edited Dec 30th 2020)

    The problem must be due to our renovated parser. Because if instead of the current page one looks at it through the page history (e.g. in rev 25) then it displays without errors.

    But even without the parsing errors, the output is ugly. Moreover, the code for the diagram in question is a weird hack, trying to include partial xypic graphics for curved and double arrows inside an Instiki array that meant to provide the remaining straight arrows. Maybe that was regarded as a necessary hack back in a time when we couldn’t include xygraphics more easily?

    There seems to be no point in salvaging this. I have now simply removed it entirely.

    What remains in the entry is the pretty-printed version of the diagram which I had added back in rev 18.

    [edit: am preparing a more conventional version, just a moment…]

    diff, v26, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeDec 30th 2020

    Okay, I have edited a bit:

    In the section “As diagrams” I have now included the expected 2-morphism diagrams, coded with a single xymatrix.

    Pointing out that the identity 2-morphisms are notationally implicit, I made this lead over to the Taiji-style version, obtained by leaving also the 1-morphisms notationally implicit.

    Then I saw that the section “As equations” didn’t state a single equation, and so I edited a bit here, to make this a little more coherent.

    Hope notation is all consistent now, it’s easy to introduce typos here.

    diff, v26, current

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