Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorDG
    • CommentTimeSep 19th 2015
    • (edited Sep 19th 2015)

    At ncatlab.org/…/category+of+simplices, Proposition 2 says that for a simplicial set XX, the category of non-degenerate simplices of XX is a reflective subcategory of the category of simplices of XX. Is that true? Does someone have a reference for that statement? At the moment I can only see it in the case that XX has the property that every face of every non-degenerate simplex of XX is itself non-degenerate.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeSep 19th 2015

    This was a mistake of mine from several years ago (look at revision 6 for the incorrect argument), which Urs tried to fix in revision 7; but it looks like he removed the incorrect argument but left in the unjustified conclusion. In fact your condition (every face of a nondegenerate simplex is nondegenerate) is probably exactly what is needed to make the incorrect argument work. Please feel free to fix the page!

    • CommentRowNumber3.
    • CommentAuthorDG
    • CommentTimeSep 20th 2015
    Done.
    • CommentRowNumber4.
    • CommentAuthorZhen Lin
    • CommentTimeSep 20th 2015

    Is there an established name for this condition? I feel like it should be called “having free degeneracies”, but I get the feeling that means something else already.

    • CommentRowNumber5.
    • CommentAuthorKarol Szumiło
    • CommentTimeSep 20th 2015

    Zhen Lin, we had an inconclusive discussion about this here.

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeSep 20th 2015

    Thanks DG! But it would be even better to replace the incorrect statement with the correct one.

    • CommentRowNumber7.
    • CommentAuthorDG
    • CommentTimeSep 21st 2015
    Oh, yes, of course ...
    Done.
Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)