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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.