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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeApr 17th 2018

Fixed some hickups in the very first sentence.

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeApr 17th 2018

One must be careful with transitive action about the empty set, but all is fine here? I guess any group acting on the empty set is a free action.

What’s the HoTT version of freeness? Something like $IsSet(\sum_{\ast: BG} V(\ast))$.

• CommentRowNumber3.
• CommentAuthorMike Shulman
• CommentTimeApr 17th 2018

I would probably state it as: for any $x$, the type of $g$ such that $g x = x$ is contractible (or, equivalently, a proposition, since it’s always inhabited by $e$).

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