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    • CommentRowNumber1.
    • CommentAuthorelif
    • CommentTimeFeb 15th 2013
    Hi! I'm working about adic completion of crossed modules but when I construct adic completion, first I need define adic topology on xmod using its maximal idea.Unfortunately; l I couldn't see how I can define???
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 16th 2013
    • (edited Feb 16th 2013)

    What is it you are looking at? Do you want to replace in the traditional definition of completion 2-groups/crossed modules for the traditonal abelian groups appearing there?

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeFeb 16th 2013

    You might want to talk to Tim Porter about this. He’s written a book about profinite crossed modules. He has a page on the nLab, or find my email at David Roberts and I can send you his details.

    • CommentRowNumber4.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 16th 2013
    • (edited Feb 16th 2013)

    You can find the pro-C completion discussed by following Profinite Algebraic Homotopy in my home page:

    http://ncatlab.org/timporter/show/HomePage

    There is a downloadable document corresponding to an old version of the book that David is referring to above, and it has a discussion of the pro-finite completion, that may be useful.

    The initial work was done by Korkes in his thesis and a joint paper in Proc. Edin Math. Soc. 1990.

    (BTW The use of ’adic’ as an adjective is awkward. This is really a construction (p-adic, M-adic, polyadic, operadic) whic constructs a new adjective from some other word. Its use in a stand alone position is very strange.)

    • CommentRowNumber5.
    • CommentAuthorelif
    • CommentTimeFeb 16th 2013
    Tim: Thank you for your comments.I will study your book is telling above more detail and if I couldn't understand some of them in it I will write here...
    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeFeb 16th 2013

    Since it seems you all know which definition exactly elif is looking for (I can guess what it is, but you all seem to be sure): It shouldn’t be hard to just state the definition here.

    • CommentRowNumber7.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 17th 2013
    • (edited Feb 17th 2013)

    @Urs. I am not at all sure what elif is looking for. The point I was making was more a linguistic one. I had noted in several papers by US authors a tendency to talk about adic completions and and have wondered what they were since there is a whole family of completions available.

    My ex-student did look at the profinite completion for crossed modules and that extends to a pro-C one. I have wondered if this is the ’right’ completion for other purposes and if I can I fill put something here or, better, on the n-lab about it. The notion of profinite completion of homotopy types is complicated and that is much harder to describe in a deffinitive way….. but in any case, I do not know what an ‘adic’ completion (of anything) is!