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Aug 22, 2018 at 21:22 comment added Tim Campion I don't know, I haven't read that bit of HTT before. I don't understand how that's relevant.
Aug 16, 2018 at 11:16 comment added Harry Gindi @TimCampion Lurie seems to use the fibrant replacement to ensure that his construction of the Yoneda embedding is a simplicial functor in 5.1.3 of HTT. Am I mistaken?
Aug 16, 2018 at 11:02 history edited Harry Gindi CC BY-SA 4.0
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Aug 16, 2018 at 5:03 comment added Tim Campion At any rate, there's no fibrant replacement functor which preserves finite limits and fibrations -- if there were, then the same argument as for the Quillen model structure would show the Joyal model structure to be right proper, which it's not.
Aug 15, 2018 at 22:48 history asked Harry Gindi CC BY-SA 4.0