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started adding a detailed "Idea" section to the page differential cohomology - nonabelian case on my personal web
currently this consists of the section The classical case of U-principal bundles and revolves around an abstract-nonsense interpretation of the Chern character
so this is in parts to be read as one more contribution in my discussion, elsewhere, with Domenico.
I think one-delooped or alike descriptive and suggestive word may be better than semiabelian, regarding specially that the latter term exists in other contexts.
thanks, right, you mentioned this in Zagreb, and I intend to change it.
In fact, I thought I should say instead "with grouplike coefficients".
following Zoran's complaint, I now changed the terminology throughout (well, I am bound to have missed some occurences).
There is now
differential cohomology - with grouplike coefficients (schreiber)
differential cohomology - with general coefficients (schreiber)
And the overview/extended abstract entry
now indicates the difference between the two
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