Timeline for A question about combinatorial model categories
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 11, 2019 at 17:11 | comment | added | Tim Campion | I'm not sure I understand your comment from Jan 11 at 14:01. It seems to me that all but the last sentence of the proof on the nlab is establishing exactly the content of Lemma 2.6.9 (in the current version of HTT). That is, it is establishing that $cof(J) = C \cap W$. What's left implicit on the nlab is the verifications that Lurie performs in the proof of Prop 2.6.10. You may be right in your comment of Jan 11 at 14:45 -- I'm not sufficiently engrossed in the details here to say. | |
| Jan 11, 2019 at 14:45 | comment | added | user09127 | As for what I do not understand in the proof of lemma 2.6.9 (again HTT new version), is the last paragraph. More precisely, I believe that lemma A.1.5.11 shows that the map $M\rightarrow N$ is in $S$, i.e. the last commutative square finishes completes the proof. If this is true, the end of the proof does what exactly? | |
| Jan 11, 2019 at 14:01 | comment | added | user09127 | I had a look again, and I must say that I still do not get why Lurie needs lemma 2.6.9 (newest HTT version), whereas the n lab does not (in the proof of the hard part of Jeff Smith's theorem.) I suspect the n lab is "cheating" somehow, but I do not get how... To be more precise, I suspect it has to do with the fact that the class of acyclic cofibrations can be generated by a set, but what would be the issue with the proof of the n lab? | |
| Jan 5, 2019 at 14:52 | comment | added | user09127 | I was referring to the older one (I definitely should have clarified...) I'll have a look at Beke's thesis first, thanks for the reference! | |
| Jan 4, 2019 at 15:24 | comment | added | Tim Campion | I just realized there is a discrepancy in the numbering between different versions of HTT. Are you referring to Corollary A.2.6.7 in the current version or Lemma A.2.6.7 in an older version? If you can clarify what you're asking about, I'd be happy to discuss it. BTW another source for the proof of Smith's theorem is the original write-up in Tibor Beke's thesis. | |
| Dec 31, 2018 at 17:02 | comment | added | user09127 | You are definitely right, I read the n lab too fast. Do you have any insight on (the end of) the proof of lemma A.2.6.7? | |
| Dec 31, 2018 at 16:03 | vote | accept | user09127 | ||
| Dec 31, 2018 at 13:43 | history | edited | Tim Campion | CC BY-SA 4.0 |
added 100 characters in body
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| Dec 31, 2018 at 13:24 | history | answered | Tim Campion | CC BY-SA 4.0 |