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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory kan lie lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes science set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

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 $e$).