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.
    • CommentAuthorMike Shulman
    • CommentTimeOct 28th 2010

    Created progroup, with remarks about the equivalence between surjective progroups and prodiscrete localic groups.

    Why do we have separate pages profinite space and Stone space which do nothing but point to each other? Is there any reason not to merge them?

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeOct 28th 2010

    Oh, and along the way I created posite.

    • CommentRowNumber3.
    • CommentAuthorTim_Porter
    • CommentTimeOct 28th 2010
    • (edited Dec 18th 2010)

    The possible justification for having two pages is that the contexts in which they live are not obviously linked. (I think that there is more of a link than the obvious one.) The contexts are profinite spaces which rubs shoulders with lots of geometry and topology, whilst Stone spaces is linked more to Boolean algebras logic, etc.

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeOct 28th 2010

    Question at posite regarding double negation topology and forcing.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeOct 28th 2010

    @Tim: hmm. I’m not entirely convinced, especially given that both are currently stubs. Could we merge them for now, and if later on it turns out that the material is bifurcating, split them up again?

    @David: I replied: yes!

    • CommentRowNumber6.
    • CommentAuthorTim_Porter
    • CommentTimeOct 28th 2010

    @Mike Just saw your nice comment on the Café and am trying to understand it. The reason I am interested (apart from the intrinsic interest of course) is that years ago I had a Postgrad, Fahmi Korkes, who looked at profinite completions of crossed modules and the general theory of profinite crossed modules. (We published a couple of short notes derived from his thesis. He was unable to write up more due to various wars etc. No need for explanation here.) I have made available a much larger draft which grew out of his work (see That version is not complete as it may be going to be published. )

    There is an interesting point that a referee for that ’book’ made relating to Dan Isaksen’s paper (Calculating limits and colimits in pro-categories, Fund. Math. 175 (2002) 175-194.) The oint is that pro- simplicial finite sets and simplicial profinite sets seem to be non-equivalent categories. (I think the point is a sort of ’phantom’ behaviour towards infinity. I am not sure what I mean by that :-(! I think I checked that the n-truncated simplicial objects are equivalent but that the equivalence may take more and more ’reindexing’ as you go up the dimensions. I am so far unable to see if this makes a big difference to the representability of the profinite homotopy types. I convinced myself that for the ’material’ I was looking at there was unlikely any problem.

    Another point perhaps worth making is that there is work by Quick (Profinite homotopy theory, Doc. Math. 13 (2003) 585-612) which gives some results that may be of interest, especially on profinite completions of ’spaces’. (I have yet to read his papers … there are others… in detail, having just skimmed them on-line. This area is big at the moment as it relates to motives etc, which may be relevant to your posting as well! .. I do not understand what the motive for motives is :-) (Yeah it was old and weak as a joke! )

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeOct 28th 2010

    Hi Mike,

    I edited your progroup slightly. Made the definition of surjective progroup a separate definition and made the first line of your proof of the theorem point pack to the previous definition.

    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeOct 28th 2010


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)