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I expanded complete Segal space a little bit and started model structure for complete Segal spaces
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.
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?
This is wrong notation for that groupoid. I am fixing it now. Thanks.
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.
Great, thanks!
I have touched model structure for complete Segal spaces, added some hpyerlinks, some more proposition environments.
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