Timeline for Does it require Reedy fibrancy when we want the totalization to be weakly equivalent to the homotopy limit?
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| Jul 3, 2015 at 16:42 | comment | added | David White | It often depends on what model you take for the holim. Nowadays it seems customary for people to implicitly fibrantly replace. If you want to know about the state of the art on these things I recommend Riehl's book, chapters 5 and 6. On page 71 she describes a setting where fibrant replacement is necessary, but I am not making this an answer because I don't have an explicit counterexample at hand (and not the time to think about it right now). I agree with Zhen Lin that I do not expect a positive answer to your question. | |
| Jul 3, 2015 at 16:33 | comment | added | David White | A list of errata is maintained by Phil here, but nothing yet in chapter 19: www-math.mit.edu/~psh/MCATL-errata-2015-01-11.pdf | |
| Jul 3, 2015 at 16:14 | comment | added | Zhaoting Wei | @ZhenLin I also expected that. But the same thing happens in Theorem 19.8.2 (but not in Theorem 19.8.3). | |
| Jul 3, 2015 at 16:12 | history | edited | Zhaoting Wei | CC BY-SA 3.0 |
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| Jul 3, 2015 at 14:18 | comment | added | Zhen Lin | I expect that it is a typographical error. | |
| Jul 3, 2015 at 14:14 | history | asked | Zhaoting Wei | CC BY-SA 3.0 |