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nLab > Latest Changes: Theta space

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 17th 2009
    • (edited Nov 6th 2012)

    did I say that I created Theta space?

    This is a really nice model. Rezk claims to have shown to get the homotopy hypothesis right for all (n,r)-categories and for both n and r ranging to \infty . If that holds water, it's quite impressive. It seems the only thing missing then is the (n+1,k+1)- Theta-space of all (n,k)-Theta spaces. Does anyone know if there is a proposal for that?

    It's also interesting how the result is a mix of globular and simplicial shapes. So in what respect does that build on/improve over Joyal's original proposal?

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 18th 2009

    I wrote out more details of the definition at Theta space. Then I added a section on the (n+1,k+1)-Theta space of all (n,k)-Theta spaces.

    I am not sure about the answer to Toby's query box at the moment.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 19th 2009

    just for the record: Charles Rezk himself has kindly joined the discussion at Theta space

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 6th 2012

    I have edited the Idea-section at Theta space. Effectively I have rewritten and then expanded the little paragraph that used to be there. I have tried to make the basic idea more transparent.

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