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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 10th 2010

    started infinity-Lie algebroid valued differential forms , since that is needed all through our discussion of oo-Chern-Weil elsewhere. But right now the entry is stubby.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 20th 2010

    expanded infinity-Lie algebroid valued differential forms

    added a discussion of how the 1-morphisms in the oo-groupoid of oo-Lie algebra value forms come from the infinitesimal gauge transformation formulas that one can find in the literature. Still have to collect the links to that literature, though.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 21st 2010
    • (edited Sep 21st 2010)

    okay, I have now added details to infinity-Lie algebroid-valued differential form on where in the literature the formulas for gauge transformation of oo-forms that I derive appear already, and in which disguise.

    Incidentally, in the process of doing so I finally understood fully the notion of “rheonomy” in the D’Auria-Fre formulation of supergravity: it’s essentially nothing but the second \infty-Ehresmann condition for super-\infty-connections locally encoding descent of curvature characteristic forms not along just the simplex bundle U×Δ kUU \times\Delta^k \to U but also along the super-simplex bundles U×Δ 1|pUU \times \Delta^{1|p} \to U. I’ll work that into the entry now.

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 21st 2010

    it’s essentially nothing but the second \infty-Ehresmann condition for super-\infty-connections locally encoding descent of curvature characteristic forms not along just the simplex bundle U×Δ kUU \times\Delta^k \to U but also along the super-simplex bundles U×Δ 1|pUU \times \Delta^{1|p} \to U.

    :D this is why I love category theory.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeSep 23rd 2010

    I reorganized the exposition a bit