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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 19th 2009
    • (edited Dec 19th 2009)

    I intend to considerbly expand the story at Atiyah Lie groupoid. But this afternoon I didn't get as far as I intended to, and now I have to quit and visit my parents. So this is to be continued. But so far I did this:

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 21st 2009
    • (edited Dec 21st 2009)

    in the section Relation to Differential Nonabelian Cohomology at Atiyah Lie groupoid details of the claim and the proof of how the Atyiah Lie groupoid At(P) \to \Pi(X) of a G-principal bundle P \to X is a quotient of the homotopy fiber of the morphism  \Pi(X) \to \mathbf{B}AUT(G) induced from a choice of connection on  P.

    I tried to present the argument in a supposedly nicely geometric fashion, with the homotopy pullback computed in terms of 2-groupoid incarnations of universal 2-bundles, but due to the restrictions of MathML diagrams it may look now a bit more awkward than it should, unfortunately.

    I'll try to polish this further, eventually.

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