Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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 nforum 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 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
   • CommentTimeJan 19th 2010
   • (edited Jan 19th 2010)
   • PermaLink
   Author: Urs
   Format: Markdownat [[interval object]] we have a section that discusses how in a category with interval object for every object there are various incarnations of its "path groupoid". We had had two such incarnations there: the first one discusses the structure of a Trimble n-category on this "path groupoid", the second one the structure of a simplicial set. I want one more such incarnation: the structure of a planar [[dendroidal set]]. A proposal for how that should work I have now typed in the new section titled currently <a href="http://ncatlab.org/nlab/show/interval+object#Dendroidal">Fundamental little 1-cubes space induced from an interval</a>. (This section title is bad, I need to think of something better...) Eventually I want to see if this can be pushed to constitute the necessary ingredients for a "May recognition principle" in a general oo-stack oo-topos: over a site C with interval object, I want for each k a _dendroidal presheaf_ that encodes something like the C-parameterized little k-cubes operad, which should act on k-fold loop oo-stacks on C. That's the motivation, at least.

   at interval object we have a section that discusses how in a category with interval object for every object there are various incarnations of its "path groupoid".

   We had had two such incarnations there: the first one discusses the structure of a Trimble n-category on this "path groupoid", the second one the structure of a simplicial set.

   I want one more such incarnation: the structure of a planar dendroidal set.

   A proposal for how that should work I have now typed in the new section titled currently Fundamental little 1-cubes space induced from an interval.

   (This section title is bad, I need to think of something better...)

   Eventually I want to see if this can be pushed to constitute the necessary ingredients for a "May recognition principle" in a general oo-stack oo-topos: over a site C with interval object, I want for each k a dendroidal presheaf that encodes something like the C-parameterized little k-cubes operad, which should act on k-fold loop oo-stacks on C.

   That's the motivation, at least.