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nLab: bibundles composition

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  1.  
    • CommentRowNumber1.
    • CommentAuthorPraphulla Koushik
    • CommentTimeJun 30th 2018
    • (edited Jul 1st 2018)

    I would like to ask question about https://ncatlab.org/nlab/show/bibundle#composition

    I have asked a question here https://mathoverflow.net/questions/303781/composition-of-bibundles asking for motivation why would one want to define composition as (E× ℋ 0F)/H(E\times_{\mathcal{H}_0}F)/H and not just E× ℋ 0FE\times_{\mathcal{H}_0}F. Is that just a choice? I guess it is not.

    https://arxiv.org/pdf/math/0702399.pdf says in page 6 says that Viewing a bibundle as relation of stacks suggests defining the composition of bibundles as (E× ℋ 0F)/H(E\times_{\mathcal{H}_0}F)/H

    I believe a little more details about what is that motivation of viewing bibundle as relation of stacks in https://ncatlab.org/nlab/show/bibundle#composition would be useful.

    Apologies if this discussion is not suitable here.

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 1st 2018
    • (edited Jul 1st 2018)

    The short answer is that the naive operation E× ℋ 0FE\times_{\mathcal{H}_0}F does not result in a bibundle. I will provide more details at the MO question before too long.

    [Also: to get the maths to render, you can edit your post and select the “Markdown+Itex” option below the text box.]

  3. Thank you @DavidRoberts.

    I am not even able to see what could go wrong for E× ℋ 0FE\times_{\mathcal{H}_0}F to be a bibundle. May be I am ignoring something important.

    • CommentRowNumber4.
    • CommentAuthorRichard Williamson
    • CommentTimeJul 2nd 2018
    • (edited Jul 2nd 2018)

    Just to say thanks for asking your question here, Praphulla, it is very welcome and suitable.

  5. Thank you @Richard Williamson:)

    Can I know who has written that part so that I can ping that author.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 3rd 2018

    Can I know who has written that part so that I can ping that author.

    There is a button “history” at the bottom of each nnLab page, which takes you to the edit history.

    Looking through it, the section “Composition” was added in rev 24 by Chenchang Zhu.

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 3rd 2018

    There is no ’pinging’ mechanism here that I am aware of (like the @ used at MO).

    Maybe it should also be added that Chenchang is not a regular nLab user and so very likely would be unaware that you want her attention, unless you email her directly.

  8. Thank you Todd Trimble and Urs.

    I will email Chenchang Zhu. :) Thank you.

    • CommentRowNumber9.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 4th 2018

    For what it’s worth, I have written something over at MathOverflow.

  10. I saw those answers. Thank you :)

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