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nLab > Latest Changes: hypercomplete (oo,1)-topos

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 22nd 2010
    • (edited May 14th 2010)

    added to hypercomplete (infinity,1)-topos a comment on how classical topos theory models these

    (motivated from our discussion here)

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 14th 2010
    • CommentRowNumber3.
    • CommentAuthorAndrew Stacey
    • CommentTimeMay 14th 2010

    (Incidentally, the problem with your first comment is the ampersand in the URL. As you’re using Markdown, the easiest way to avoid this problem is to include links using Markdown’s syntax. Thus “(motivated from our discussion here)”.)

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 14th 2010

    As you’re using Markdown, the easiest way to avoid this problem is to include links using Markdown’s syntax.

    Thanks, Andrew, I’ll try to remember that. But that first comment was written and displayed correctly before the software was changed.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 27th 2010
    • (edited May 27th 2010)

    Statement and proof of the main proposition in the section on models.

    (Needs a bit of polishing and deserves a bit of expansion here and there, but have to run now.)

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMay 27th 2010

    hm, the \widehat-notation comes out almost invisible…

    • CommentRowNumber7.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 28th 2010

    I agree on the \widehat - I tried using it elsewhere and it was indistinguishable from \hat.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJun 18th 2010

    I have typed out (even) more details of the proof that the Joyal-Jardine model structure presents hypercomplete (oo,1)-toposes here.

    • CommentRowNumber9.
    • CommentAuthoralex
    • CommentTimeMay 14th 2013
    I am not an expert on (∞,1)-topoi but as far as I have understood I find the following quite confusing:

    The first observation says that "An (∞,1)-topos that has enough points is hypercomplete." The term 'enough points' is explained on http://ncatlab.org/nlab/show/point+of+a+topos but it refers to classical topoi, where 'enough points' can be used to test for isomorphism. However, in the cited reference in HTT, Lurie defines having enough points as being able to test equivalences on those and I believe that this can be a different thing. So one should probably add an explanation of 'enough points' to this entry?
    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeMay 14th 2013
    • (edited May 14th 2013)

    True, that was hidden a bit between the lines. I have now added more clarifying (hopefully) comments here.

1 to 10 of 10

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