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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeFeb 16th 2010
   • (edited Oct 23rd 2012)
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   Author: Urs
   Format: MarkdownI expanded [[complete Segal space]] a little bit and started [[model structure for complete Segal spaces]]

   I expanded complete Segal space a little bit and started model structure for complete Segal spaces

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 12th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexI 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.

   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.

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeApr 3rd 2012
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   Author: Mike Shulman
   Format: MarkdownItexIn 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?

   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?

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeApr 3rd 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexThis is wrong notation for that groupoid. I am fixing it now. Thanks.

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

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeApr 3rd 2012
   • (edited Apr 3rd 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI 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](http://ncatlab.org/nlab/show/model+structure+for+dendroidal+complete+Segal+spaces#RelationToDendroidalSets).

   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.

6. • CommentRowNumber6.
   • CommentAuthorMike Shulman
   • CommentTimeApr 3rd 2012
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   Author: Mike Shulman
   Format: MarkdownItexGreat, thanks!

   Great, thanks!

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeOct 23rd 2012
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   Author: Urs
   Format: MarkdownI have touched _[[model structure for complete Segal spaces]]_, added some hpyerlinks, some more proposition environments.

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