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nLab > Latest Changes: higher homotopy van Kampen theorem

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 26th 2010

    I added to higher homotopy van Kampen theorem the statement of the theorem by Jacob Lurie.

    • CommentRowNumber2.
    • CommentAuthorronniegpd
    • CommentTimeMar 20th 2017
    The result of Lurie is called a higher homotopy van Kampen theorem though it looks like a much older small simplex theorem.

    A notable feature of the HHSvKTs with which I have been involved, and indeed in the traditional vKT, is the key notion of connected and its use in the statement and proof of the theorems, But this terms does not occur in some of the other statements of results labelled as in this class of theorems.

    On this basis alone, the theorems would seem to be of very different types.
    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeMar 21st 2017

    I think it makes sense to call any theorem of the sort “fundamental nn-groupoid functor preserves some colimits” a “higher van Kampen theorem”.

    • CommentRowNumber4.
    • CommentAuthorDylan Wilson
    • CommentTimeNov 15th 2022
    As far as I can tell, Lurie's (non-stratified) Van Kampen theorem is exactly Proposition A.5 of Segal's paper on foliations: https://core.ac.uk/download/pdf/82283884.pdf

    Does that look right to y'all?

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