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I’ve been thinking about generalizing the Cech-Delign double complex to the case where $U(1)$ is replaced by some Lie group, $G$, and $\mathbb{R}$ is replaced with $\mathfrak{g}$. I came across this post on Nonabelian Weak Deligne Hypercohomology by Urs a while back and was wondering if his musing was ever fully considered/resolved?
For full context of why I’m considering this: I was working on a project during my PhD that I’d like to eventually publish, but I constructed an element in a (Hochschild-like) curved dga with a Chen map to holonomy (path or surface) which is a chain map and map of algebras. It was suggested that this is not enough of a “result” unless I could find the right notion of equivalence to fully flesh out this map. I was hoping that some resolution of the referenced article above could allow me to put my work in that context.
P.S. This is my first post here so my apologies if I made a cultural error.
Hi, good that you are writing here!
The ideas underlying these old notes eventually evolved into this here:
Fiorenza, Schreiber, Stasheff,
“Cech cocycles for differential characteristic classes – An $\infty$-Lie theoretic construction”,
Adv. Theor. Math. Phys. 16 (2012) 149-250 (arXiv:1011.4735)
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