Timeline for detecting weak equivalences in a simplicial model category II
Current License: CC BY-SA 4.0
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| S Sep 13, 2018 at 10:58 | history | bounty ended | Let | ||
| S Sep 13, 2018 at 10:58 | history | notice removed | Let | ||
| Sep 11, 2018 at 19:42 | vote | accept | Let | ||
| Sep 11, 2018 at 19:03 | answer | added | dhy | timeline score: 3 | |
| S Sep 11, 2018 at 17:30 | history | bounty started | Let | ||
| S Sep 11, 2018 at 17:30 | history | notice added | Let | Canonical answer required | |
| Sep 7, 2018 at 2:55 | comment | added | Tim Campion | Probably this can be proven if every object is cofibrant. So when looking for counterexamples, it's probably best to look at simplicial model categories where not every object is cofibrant. | |
| Sep 6, 2018 at 16:36 | comment | added | Valery Isaev | I agree with OP. The question is not that simple and the answer might as well be no. It seems that @skd's suggestion doesn't work because we need to take cofibrant fibrant replacements of a and b which belong to $R$, but I think we can't choose such a replacement in general. | |
| Sep 6, 2018 at 13:31 | history | edited | Let | CC BY-SA 4.0 |
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| Sep 5, 2018 at 7:27 | comment | added | Let | @skd I'm a beginner in the field, I tried your suggestion, I was unable to provide a correct proof. I feel I'm missing some thing... Any help with more detail is welcome. | |
| Sep 4, 2018 at 21:46 | history | edited | David White | CC BY-SA 4.0 |
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| Sep 4, 2018 at 21:29 | comment | added | skd | Unless I've misunderstood, essentially the same argument as in Hirschhorn's book should give an affirmative answer to your question. (First do a cofibrant-fibrant replacement of a and b, then do a fibrant replacement of w; apply the argument to this replacement of w.) | |
| Sep 4, 2018 at 19:13 | history | edited | Let |
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| Sep 4, 2018 at 19:03 | history | asked | Let | CC BY-SA 4.0 |