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1. I added a reference to a paper of mine

Amnon Yekutieli

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• CommentTimeAug 15th 2020

• Jinpeng An. Zhengdong Wang, Nonabelian cohomology with coefficients in Lie groups,Trans. Amer. Math. Soc. 360 (2008), 3019-3040 (doi:10.1090/S0002-9947-08-04278-5)
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• (edited Aug 15th 2020)

For citation purposes, what’s a good (textbook) account that makes explicit both the concept of non-abelian cohomology and its representation by classifying spaces (under suitable conditions)

I am asking, because the literature on “non-abelian cohomology” tends to jump to arcane properties before ever saying clearly what the (simple) main structure of the general theory actually is. As a result, it is hard to tell a reader “see reference XYZ”, because if they don’t already know about the topic, they might not even recognize that XYZ is about this topic.

The article Roberts-Stevenson 12 above stands out in this respect, as it does state these general principle on the first three pages, even if not quite in an expository way.

But ignoring higher groups and stuff, just focusing on the ancient theory. What’s your preferred textbook(-style) reference that makes clear that non-abelian cohomology is a thing and that its ultimately about maps into classifying spaces?

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• CommentTimeAug 15th 2020

I have tried to give some more logical order to the list of references.

Now I have introduced 3 subsections under “References”, correspondoing to discussion in homotopical dimensioon 1, 2, $\infty$, respectively.

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• (edited Sep 2nd 2020)

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• Carlos Simpson, Algebraic aspects of higher nonabelian Hodge theory, in: Fedor Bogomolov, Ludmil Katzarkov (eds.), Motives, polylogarithms and Hodge theory, Part II (Irvine, CA, 1998), Int. Press Lect. Ser., 3, II, Int. Press, 2002, 2016, 417-604. (arXiv:math/9902067, ISBN:9781571462909)
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• CommentTimeJan 19th 2021
• (edited Jan 19th 2021)

(since unstable operations on stable cohomology is really operations on their image in non-abelian cohomology)

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• CommentTimeJul 14th 2021