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1. • CommentRowNumber1.
   • CommentAuthorMirco Richter
   • CommentTimeJan 31st 2012
   • PermaLink
   Author: Mirco Richter
   Format: MarkdownItexSuppose we have the sequence of sets $\mathbb{R}$, $\mathbb{R}^2$, $\mathbb{R}^3$, ... Is there a Kan simplicial structure on this sequence of sets, that is not $n$-coskeletal for some $n \in \mathbb{N}$? To be more precise, is there a simplicial set (functor) $R$ with $R([n]) = \mathbb{R}^{n+1}$ that is not $n$-coskeletal for some $n \in \mathbb{N}$? And very closely related: is there a simplicial set (functor) $R$ with $R([n]) = \mathbb{R}^{n}$ (with $R([0]))=\{0\}$), that is not $n$-coskeletal for some $n \in \mathbb{N}$ ?

   Suppose we have the sequence of sets $\mathbb{R}$, $\mathbb{R}^2$, $\mathbb{R}^3$, … Is there a Kan simplicial structure on this sequence of sets, that is not $n$-coskeletal for some $n \in \mathbb{N}$?

   To be more precise, is there a simplicial set (functor) $R$ with $R([n]) = \mathbb{R}^{n+1}$ that is not $n$-coskeletal for some $n \in \mathbb{N}$?

   And very closely related: is there a simplicial set (functor) $R$ with $R([n]) = \mathbb{R}^{n}$ (with $R([0]))=\{0\}$), that is not $n$-coskeletal for some $n \in \mathbb{N}$ ?

2. • CommentRowNumber2.
   • CommentAuthorMirco Richter
   • CommentTimeJan 31st 2012
   • PermaLink
   Author: Mirco Richter
   Format: MarkdownItexOr is there a theorem that rules it out? What about general "existance theorems" for Kan simplicial structures?

   Or is there a theorem that rules it out?

   What about general “existance theorems” for Kan simplicial structures?