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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeApr 17th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexFixed some hickups in the very first sentence. <a href="https://ncatlab.org/nlab/revision/diff/free+action/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/free+action/12">v12</a>, <a href="https://ncatlab.org/nlab/show/free+action">current</a>

   Fixed some hickups in the very first sentence.

   diff, v12, current

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeApr 17th 2018
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   Author: David_Corfield
   Format: MarkdownItexOne 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 $IsSet(\sum_{\ast: BG} V(\ast))$.

   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 $IsSet(\sum_{\ast: BG} V(\ast))$.

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeApr 17th 2018
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   Author: Mike Shulman
   Format: MarkdownItexI 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 $e$).

   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 $e$).