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    • CommentRowNumber1.
    • CommentAuthorMirco Richter
    • CommentTimeJan 31st 2012

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

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

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

    • CommentRowNumber2.
    • CommentAuthorMirco Richter
    • CommentTimeJan 31st 2012

    Or is there a theorem that rules it out?

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