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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 $t_! \dashv t^!$ using the functor

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

However, Joyal and Tierney define this adjunction using instead

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

where $(\Delta^l)'$ is the nerve of the groupoid freely generated by $[l]$. 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 “$\Delta_J[n]$” (for J-T’s ” $(\Delta^n)'$ “) 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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