Timeline for Model category structure on spectra
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 3, 2019 at 13:46 | comment | added | Tintin | Thanks again for the answer, Dmitri. My imprecision reflects my ignorance :) I didn't know about that. Thanks a lot also for the edit, I learnt with it! | |
| Apr 3, 2019 at 13:41 | history | edited | Dmitri Pavlov | CC BY-SA 4.0 |
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| Apr 3, 2019 at 13:39 | comment | added | Dmitri Pavlov | @Tintin: The imprecision in my answer merely reflects the imprecision in the original post, which doesn't specify which of the many different categories Spt(S) of motivic spectra is being used. Accordingly, I made a choice. In fact, if you pick a model category Spt(S) that is not right proper, then a model structure with all objects fibrant simply does not exist. I edited my answer accordingly. | |
| Apr 3, 2019 at 10:46 | vote | accept | Tintin | ||
| Apr 3, 2019 at 10:45 | comment | added | Tintin | Thank you very much for the answer, Dmitri, which has solved my doubt. I agree also with Fernando, I think it would be nice for future readers to introduce that precision in your answer. Would you agree? For example: "Essentially yes. According to[...] there is a category $\mathrm{Alg} \mathbf{Spt}(S)$ with a model structure producing $\mathbf{SH}$ and where all objects are fibrant. This model category $\mathrm{Alg} \mathbf{Spt}(S)$ is Quillent equivalent to $ \mathbf{Spt}(S)$". Or something analogous. In the problem I am working with, this precision is not totally superfluous. Thanks! | |
| Apr 3, 2019 at 10:26 | vote | accept | Tintin | ||
| Apr 3, 2019 at 10:26 | |||||
| Apr 3, 2019 at 10:19 | vote | accept | Tintin | ||
| Apr 3, 2019 at 10:19 | |||||
| Apr 3, 2019 at 2:51 | comment | added | Fernando Muro | There's a subtle difference between having a model structure on a given category where all objects and fibrant and with given homotopy category and being Quillen equivalent to a model category where all objects are fibrant. | |
| Apr 2, 2019 at 17:51 | history | answered | Dmitri Pavlov | CC BY-SA 4.0 |