Timeline for Monoidal Model Categories with Suspension Functor
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 30, 2012 at 0:58 | vote | accept | Jonathan Beardsley | ||
| Oct 30, 2012 at 0:32 | answer | added | David White | timeline score: 3 | |
| Oct 29, 2012 at 23:45 | comment | added | Marc Hoyois | For a treatment of stabilization of $(\infty,1)$-categories, check out the first chapter of Lurie's Higher Algebra. Spectra are defined there for any $(\infty,1)$-category with finite limits, so you really don't need much. | |
| Oct 29, 2012 at 20:31 | comment | added | Fernando Muro | See Hovey's Spectra and symmetric spectra in general model categories, J. Pure Appl. Alg. 165 (2001), 63-127. | |
| Oct 29, 2012 at 20:14 | comment | added | Tom Goodwillie | But it might not be of much use unless you assume a little more, like that filtered (or at least sequential) hocolims in $M$ commute with finite holims. Without that it's not even clear to me what would be a useful definition of weak equivalence of spectra. | |
| Oct 29, 2012 at 20:06 | history | undeleted | Jonathan Beardsley | ||
| Oct 29, 2012 at 20:06 | history | deleted | Jonathan Beardsley | ||
| Oct 29, 2012 at 19:57 | comment | added | Aaron Mazel-Gee | In any model category $M$ you have $\Sigma X = \mbox{hocolim}(\ast \leftarrow X \rightarrow \ast)$. Then you can define a category $S^M$ of internal spectra in the same way as you do for spaces, and this comes with a stabilization functor $\Sigma^\infty:M \rightarrow S^M$. | |
| Oct 29, 2012 at 19:47 | history | asked | Jonathan Beardsley | CC BY-SA 3.0 |