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

Great, 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.

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

]]>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?

]]>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.

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

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