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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeAug 31st 2010

    I noticed that augmented simplicial set did not point anywhere, so i created the entry. But have no energy to put anything of substance there right now.

    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeSep 1st 2010

    I started to put down some details, but I suddenly have to go, so I’ll finish it in a few hours.

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 1st 2010
    • (edited Sep 1st 2010)

    I put in the observation that an augmented simplicial set is the same as an ordinary simplicial set with a map to a constant simplicial set. Also, there is an isomorphism of categories sSet +sSet 2× sSetSetsSet_+ \simeq sSet^\mathbf{2}\times_{sSet} Set, but I didn’t put this in yet.

    • CommentRowNumber4.
    • CommentAuthorTobyBartels
    • CommentTimeSep 1st 2010

    I finally filled in my gaps.

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 1st 2010

    regarding degeneracy maps, there isn’t one from X 1X_{-1} to X 0X_0, and there only one face map the other way. The sentence about ’for each natural number’ dealing with the case n=1n=-1 for face maps is a bit slippery and requires a bit too much negative thinking that early in the article, IMHO. I like the exposition otherwise, and I can’t think how to nicely rewrite it at the moment.

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 1st 2010

    Also we should put in that every simplicial set XX is canonically augmented over π 0(X)\pi_0(X).

    • CommentRowNumber7.
    • CommentAuthorTobyBartels
    • CommentTimeSep 1st 2010

    Done. I actually put in both the left and right adjoints to the underlying unaugmented simplicial set.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeSep 1st 2010

    I have expanded the entry more.

    • Moved all that was in the Idea-section to the Definition section and wrote a more genuine Idea-section.

    • Exapnded in the Definition-section a bit, in particular highlighted the new simplicial identity in degree -1.

    • Started a section with examples.

    • CommentRowNumber9.
    • CommentAuthoratmacen
    • CommentTimeMay 18th 2019
    There’s a problem for me with the adjunction graphic. The text “Layer 1” appears over some other stuff. It looks like a problem with an SVG.
    • CommentRowNumber10.
    • CommentAuthoratmacen
    • CommentTimeMay 18th 2019
    Odd. It looks fine in both the previous revision and the diff.
    • CommentRowNumber11.
    • CommentAuthoratmacen
    • CommentTime7 days ago
    Re #9: I’m talking about the one in the “Properties” section.
    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTime7 days ago

    Maybe you should add another item to the bug report list

    Just to say that, from what Richard kept saying, currently the main version of any page is rendered using his modified rendering engine, while all pages in history etc. use the old engine. That should explain why some effect appears here but not there.

    • CommentRowNumber13.
    • CommentAuthoratmacen
    • CommentTime7 days ago
    Thanks for that info, Urs. I’ve added this to the new bug list.
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