Timeline for Well-Generated Localized Triangulated Categories
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 13, 2012 at 3:12 | comment | added | Jonathan Beardsley | @Akhil no problem! I'm pretty sure I was sitting behind you at the Dan Quillen memorial conference! :-) | |
| Oct 12, 2012 at 22:57 | comment | added | Akhil Mathew | John: Thanks for these references! I'll have a look. | |
| Oct 3, 2012 at 12:58 | comment | added | Jonathan Beardsley | Hey @Akhil I don't really know why, but the proof/explanation is in appendix B (specifically Cor. B.13) of Hovey and Strickland's "Morava K-theoriesand Localisation" which I believe can be found here: hopf.math.purdue.edu/Hovey-Strickland/kn.pdf This is also discussed briefly in Example 3.5.4(a) of Hovey, Palmieri and Strickland's "Axiomatic Stable Homotopy Theory" (math.rochester.edu/people/faculty/doug/otherpapers/…) although I'm sure there are people on this site who can explain it perhaps intuitively. | |
| Oct 3, 2012 at 11:28 | comment | added | Akhil Mathew | Why does the $MU$-localization of the stable homotopy category have no small objects? | |
| Oct 2, 2012 at 22:40 | comment | added | Jonathan Beardsley | @Fernando okay great thanks! I sort of thought that might be the one I needed :-) | |
| Oct 2, 2012 at 22:39 | comment | added | Fernando Muro | The first part is in Neeman's book. It's actually the point of well generated categories. Cofibrantly generated categories are not closed under quotients, but well generated categories are. The set theoretical assumption is called Vopenka's principle. Look at the last papers by Casacuberta & co. | |
| Oct 2, 2012 at 22:28 | comment | added | Jonathan Beardsley | Thanks @Fernando! Is this somewhere in Neeman's book? Also, do you happen to know which set-theoretic principles must be assumed? | |
| Oct 2, 2012 at 22:21 | comment | added | Fernando Muro | The quotient of a well generated category by a localizing subcategory generated by a set is again well generated. All localizing subcategories are generated by sets if we assume some set-theoretical axioms. | |
| Oct 2, 2012 at 21:57 | history | asked | Jonathan Beardsley | CC BY-SA 3.0 |