Timeline for "non-Bousfield" localisations of model categories
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 31, 2013 at 10:36 | comment | added | mmm | thanks for your responses. I just saw them now, (and do not get email notifications), and not sure if you'll ever see my response... | |
| Jul 31, 2013 at 10:35 | comment | added | mmm | Quite the opposite, I want cofibrations to change. The point is, there is a sequence of related model category structures (with more and more cofibrations), and I wanted to see whether it is a sequence of localisations | |
| Nov 10, 2012 at 0:28 | comment | added | David White | If my comment above is correct, then the Bousfield localization (if it exists) will be the localization in your sense, by its well-known universal property. However, your type should always exist (because the class of $M'$ is nonempty, so you can just take the one "closest" to $M$) even if Bousfield localization does not. But because you haven't required the cofibrations in $M$ and $M_S$ to match up, I'm not sure if yours is good for anything. Still, +1 since it got me thinking. | |
| Nov 10, 2012 at 0:22 | comment | added | David White | I believe your universal property will force the underlying categories to be equal. I mean, you could take $M'$ to be the model structure on $M$ where the weak equivalences are the isomorphisms and all maps are both fibrations and cofibrations. | |
| Feb 10, 2012 at 21:40 | comment | added | Jonathan Beardsley | If I'm not mistaken, it's essentially a sort of set-theoretic condition on the class of morphisms we want to localize at? That is, we basically take (homotopy) colimits over acyclics w.r.t. to our class W of morphisms, and if that class is generated under homotopy colimits by a set, then our localization exists. | |
| Apr 27, 2011 at 12:13 | history | asked | mmm | CC BY-SA 3.0 |