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nLab > Latest Changes: product of simplices

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 22nd 2021

    added pointer to:

    diff, v18, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 10th 2021

    added pointer to:

    diff, v19, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 10th 2021

    added pointer to the original

    • Samuel Eilenberg, Saunders MacLane, (5.3) in: On the groups H(Π,n), I, Ann. of Math. (2) 58, (1953), 55–106. (jstor:1969820)

    following:

    and cross-linked with Eilenberg-Zilber map

    diff, v19, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJul 11th 2021
    • (edited Aug 28th 2021)

    I have expanded (here) the section on examples a tad, making more explicit the form of the non-degenerate simplices in Δ[1]×Δ[n] for general n.

    In the course of this I have worked a bit on the outline of the entry. I have tried to disentangle general discussion of products of simplicial sets in a first section, from discussion of non-degenerate cells in a second session. I have also turned some really small subsections into numbered remarks, instead. There is still more one could do along these lines, but I’ll leave it as is for now.

    diff, v20, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJul 11th 2021

    Added also an example (here) with a tikzcd diagram showing all the non-degenerate simplices in Δ[1]×Δ[1].

    diff, v21, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 12th 2021

    I have re-written the proposition (here) on the non-degenerate simplices in Δ[p]×Δ[q], now highlighting the transparent characterization as the strictly monotone morphisms of posets

    Δ[p+q]⟶Δ[p]×Δ[q].

    This immediately yields the path-notation, for which I added an illustrating tikz-graphics.

    diff, v23, current

    • CommentRowNumber7.
    • CommentAuthorTim_Porter
    • CommentTimeJul 12th 2021

    Typo fixed

    diff, v24, current

  8. Fixing what I believe is a typo. First time editor.

    Kevin Buzzard

    diff, v26, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeAug 28th 2021

    Yes, thanks!!

    • CommentRowNumber10.
    • CommentAuthorTim_Porter
    • CommentTimeAug 28th 2021

    There is an image that is not displaying at all. (It seems to have been produced by presheaf.com ….. but I do not see it at all.

    (I also removed a } near the non-image.

    diff, v28, current

    • CommentRowNumber11.
    • CommentAuthorRodMcGuire
    • CommentTimeAug 28th 2021
    • (edited Aug 28th 2021)

    I’m seeing a lot of broken image links from presheaf.com which seems to be down right now.

    I can find no notice that Vlad Patryshev has abandoned that site and since he is active on twitter I presume it is only a temporary outage.

    https://github.com/vpatryshev/presheaf

    All of those images need to be locally rendered, which can be done now.

    EDIT: fixed presheaf.com link

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeAug 28th 2021

    Tim, these images are from your original version of the entry, aren’t they?

    I did a lot of cleaning up here (or I tried), but I left untouched, for the moment, your material in what is now Section 4 and Section 5, which is where the broken images reside.

    • CommentRowNumber13.
    • CommentAuthorTim_Porter
    • CommentTimeAug 28th 2021
    • (edited Aug 28th 2021)

    I have not used presheaf.com as far as I can recall. If I have time, I will look back to see when they were added and to try to see what they were intended to be. The problem would seem to be a tikzcddiagram the gives an error message. I do not use tikzcd at present and would not have used it for that diagram. I still use xypic.

    I checked back, and the original diagram was done in xypic but using codecogs so someone replaced it.

    • CommentRowNumber14.
    • CommentAuthorTim_Porter
    • CommentTimeAug 30th 2021
    • (edited Aug 30th 2021)

    I have replaced the faulty diagram with one produced on xypic. (The old one was I think a copy of the one that was given above it.) I am not sure how to alter the spacing which is a bit too expansive.

    BTW the editing process is calling presheaf.com and seems unable to connect or to terminate.

    diff, v30, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeDec 3rd 2022

    Coming back to this entry, I have merged the takeaway message of the previously verbose explanation of the shuffle-perspective into the section “Characterization” (here, starting with adding shuffle labels to the big example tikzcd-diagram).

    In doing so I spotted that the last proposition of this section had been wrong all along, and I have fixed it. I believe. Have to run now, though, will polish this up later.

    diff, v32, current

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeDec 4th 2022

    I went through the Examples-section (here) and added to all path-expressions the corresponding shuffle example.

    (The list of examples is maybe a little repetitive now, but anyway.)

    diff, v34, current

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeDec 4th 2022

    I am finally removing from this entry the subsections

    “The poset of (p,q)-shuffles” and “The Anti-Lex order”

    and moving them to the entry shuffle, instead (as there is nothing directly about simplices in these sections).

    diff, v34, current

1 to 17 of 17

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