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nLab > Latest Changes: universal coefficient theorem

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 26th 2010
    • (edited Oct 22nd 2012)
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMar 1st 2011

    added a little bit of further detail to universal coefficient theorem

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 22nd 2012
    • (edited Oct 22nd 2012)

    added to universal coefficient theorem a new subsection In ordinary homology with statement and proof of the theorem in ordinary homology.

  4. Corrected a typo : H^\bullet(B,N_2) instead of H^\bullet(A,N_2) in the “In terms of cohomology” section

    Anonymous

    diff, v40, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeOct 22nd 2020

    added the example

    H •(−;ℚ)≃Hom ℤ(H •(−;ℚ);ℚ). H^\bullet \big( -; \, \mathbb{Q} \big) \;\; \simeq \;\; Hom_{\mathbb{Z}} \Big( H_\bullet\big(-;\,\mathbb{Q} \big); \, \mathbb{Q} \Big) \,.

    (here)

    diff, v41, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeOct 22nd 2020

    Now the entry doesn’t display, but throws an error message I suspect this is due to a line that has been there before, but I haven’t identified it yet…

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeDec 20th 2020

    Just drawing attention to #6 again.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeDec 20th 2020
    • (edited Dec 20th 2020)

    Thanks for the reminder. I just had another go at it, but still couldn’t identify the offending line.

    But I notice that this entry has lot of fancy Instiki code in it that we don’t usually use (written by Andrew Stacey, way back). Maybe some of that code doesn’t work well with our renovated parser. But I am just guessing here.

    • CommentRowNumber9.
    • CommentAuthorDmitri Pavlov
    • CommentTimeDec 20th 2020
    • (edited Dec 20th 2020)
    There is no offending line. This is a bug in Instiki, which incorrectly generates nested tables of contents.

    Specifically, when nesting lists like <ul> in the table of contents,
    the interior <ul> must appear inside an <li> element, but Instiki places it outside of all <li> elements, directly inside another <ul> element, which is not legitimate.

    Another serious bug in the Instiki engine is that if a section title contains a hyperlink (like in this case),
    the engine attempts to generate an <a> element inside another <a> element,
    which is not legitimate. This can be resolved by removing hyperlinks from the table of contents.
    • CommentRowNumber10.
    • CommentAuthorDmitri Pavlov
    • CommentTimeDec 20th 2020

    Trying to fix the problem.

    diff, v43, current

    • CommentRowNumber11.
    • CommentAuthorDmitri Pavlov
    • CommentTimeDec 20th 2020

    Again…

    diff, v43, current

    • CommentRowNumber12.
    • CommentAuthorDmitri Pavlov
    • CommentTimeDec 20th 2020
    So the even more serious problem (which actually breaks the XML parsing)
    is that the closing tag </ul> is inserted twice right before the section
    freeness_and_flatness: Freeness and Flatness

    This results in the list ending prematurely, and the rest of the table of contents cannot be parsed.
    • CommentRowNumber13.
    • CommentAuthorRichard Williamson
    • CommentTimeDec 21st 2020
    • (edited Dec 21st 2020)

    Urs was essentially right that the problem here was use of some weird theorem environments. I have worked around this for the moment by changing the header level of these to depth 7; they don’t parse as intended, but at least do not break the page. I’ll add a ’Statement’ theorem environment when I get a chance to fix this properly.

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeDec 21st 2020
    • (edited Dec 21st 2020)

    Thanks everyone for looking into it!

    I didn’t notice that there were hyperlinks in section headers here. Independently of whether these are parsed properly or not, we should probably avoid them – and remove them where not previously avoided – if not for technical reasons then as a matter of style and usability.

  15. Re #14: I agree!

  16. I have now added ’Statement’ and ’Assumption’ theorem environments (the code change can be seen at github), and fixed the page properly accordingly, as promised in #13.

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