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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 16th 2010
    • (edited Oct 23rd 2012)
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMar 12th 2012

    I added to the Definition-section at model structure for complete Segal spaces the explicit statement of its nature as a left Bousfield localization of the Reedy model structure. In the course of this I reorganized the section somewhat.

    Hoping to come back to this entry later to prettify it more.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeApr 3rd 2012

    In the section on “relation to quasi-categories”, the page model structure for complete Segal spaces defines the adjunction t !t !t_! \dashv t^! using the functor

    t(k,l)=Δ k×Ex Δ l.t(k,l) = \Delta^k \times Ex^\infty \Delta^l.

    However, Joyal and Tierney define this adjunction using instead

    t(k,l)=Δ k×(Δ l).t(k,l) = \Delta^k \times (\Delta^l)'.

    where (Δ l)(\Delta^l)' is the nerve of the groupoid freely generated by [l][l]. Are these the same for some reason?

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 3rd 2012

    This is wrong notation for that groupoid. I am fixing it now. Thanks.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeApr 3rd 2012
    • (edited Apr 3rd 2012)

    I have changed the notation to “Δ J[n]\Delta_J[n]” (for J-T’s ” (Δ n)(\Delta^n)' “) to harmonize with the notation of the more recent discussion at model structure for dendroidal complete Segal spaces here.

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeApr 3rd 2012

    Great, thanks!

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeOct 23rd 2012

    I have touched model structure for complete Segal spaces, added some hpyerlinks, some more proposition environments.

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