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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 categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry 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 lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory object 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 set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMar 24th 2010
   • (edited Mar 24th 2010)
   • PermaLink
   Author: Urs
   Format: Markdowncreated reference-entry on [[David Roberts]]' thesis: * [[Fundamental Bigroupoids and 2-Covering Spaces]] and linked to it from [[Whitehead tower in an (infinity,1)-topos]] (David, I slightly edited your nLab-page, accordingly)

   created reference-entry on David Roberts' thesis:

   • Fundamental Bigroupoids and 2-Covering Spaces

   and linked to it from Whitehead tower in an (infinity,1)-topos

   (David, I slightly edited your nLab-page, accordingly)

2. • CommentRowNumber2.
   • CommentAuthorDavidRoberts
   • CommentTimeMar 24th 2010
   • PermaLink
   Author: DavidRoberts
   Format: TextThanks, Urs! I had a look at [[Whitehead tower in an (infinity,1)-topos]] and the sections I wrote and they are sketchy as. When I get some time I will tidy things up.

   Thanks, Urs! I had a look at Whitehead tower in an (infinity,1)-topos and the sections I wrote and they are sketchy as. When I get some time I will tidy things up.
3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMar 24th 2010
   • (edited Mar 24th 2010)
   • PermaLink
   Author: Urs
   Format: Markdown> When I get some time I will tidy things up. That would be nice! I was thinking about working on polishing these paragraphs, but seem to have run out of energy. You should emphasize that the ordinary pullback of the tangent n-groupoid is just one (useful) model of the homotopy pullback of the point. The homotopy pullback perspective gives the abstract concept, the pullback of the tangent n-groupoid a nice convenient concrete realization. Motivated by your remarks there, I want to add now somwehere a discussion of how the coskeleton operation on sSet models the notion of n-truncation of objects in the oo-topos <latex> \infty Grpd </latex>. That'll be it for today then, for me.

   When I get some time I will tidy things up.

   That would be nice! I was thinking about working on polishing these paragraphs, but seem to have run out of energy.

   You should emphasize that the ordinary pullback of the tangent n-groupoid is just one (useful) model of the homotopy pullback of the point. The homotopy pullback perspective gives the abstract concept, the pullback of the tangent n-groupoid a nice convenient concrete realization.

   Motivated by your remarks there, I want to add now somwehere a discussion of how the coskeleton operation on sSet models the notion of n-truncation of objects in the oo-topos . That'll be it for today then, for me.