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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJul 20th 2020
• (edited Jul 20th 2020)

starting a stub, for the moment just to record references.

There is a plethora of constructions in the literature. Has anyone discussed in detail if/how these relate to the evident general abstract definition (maps of $\infty$-stacks from the given geometric groupoid to the Deligne complex)?

I see that some authors, like Redden, partially go in this direction, but I haven’t seen yet a comprehensive account to this extent.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeNov 12th 2020

• Joe Davighi, Ben Gripaios, Oscar Randal-Williams, Differential cohomology and topological actions in physics (arXiv:2011.05768)
• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeNov 12th 2020

• Joe Davighi, Ben Gripaios, Oscar Randal-Williams, Differential cohomology and topological actions in physics (arXiv:2011.05768)
• CommentRowNumber4.
• CommentAuthorDavid_Corfield
• CommentTimeNov 12th 2020

Is there anything in this that we couldn’t have picked up from your work?

• CommentRowNumber5.
• CommentAuthorDmitri Pavlov
• CommentTimeNov 12th 2020

Attempted to clarify the relationship between the definitions of Kübel-Thom and Redden vs. Gomi in the references.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeNov 12th 2020

The last paragraph of the Idea section is also meant to deal with this.

I seem to remember that Gomi’s definition is fine for finite groups?

• CommentRowNumber7.
• CommentAuthorDmitri Pavlov
• CommentTimeNov 12th 2020

Yes, Gomi’s definition only works for finite groups. (So, basically, orbifolds.)

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeNov 12th 2020

Thanks, so that agrees with what is says in the main text. I have added the qualification about finite groups to Gomi’s reference item.