Timeline for Stable presentable categories as module categories
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 9, 2009 at 0:52 | vote | accept | Reid Barton | ||
| Nov 9, 2009 at 0:51 | comment | added | Reid Barton | Corollary B.13 of the reference [HS99] gives examples of what I presume are stable presentable categories without any nonzero compact objects. | |
| Nov 9, 2009 at 0:44 | comment | added | Charles Rezk | I don't have a ready example in the case where you drop the hypothesis of compactness. If you form the localization of spectra with respect to a homology theory E, the localization L_E(S) of the sphere spectrum is a generator for this stable homotopy theory, but in general L_E(S) is not compact. But this doesn't preclude the existence of some other compact generator, and that actually happens in some cases, e.g., E= a Morava K-theory. | |
| Nov 9, 2009 at 0:34 | history | edited | Charles Rezk | CC BY-SA 2.5 |
Corrected.
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| Nov 9, 2009 at 0:33 | comment | added | Charles Rezk | Ah. I should have said "compact generators", as that appears the condition Schwede-Shipley require. So "presentable" implies "set of generators", but "compact generators" is much more special. | |
| Nov 9, 2009 at 0:24 | comment | added | Reid Barton | I think that "has a set of generators" is implied by "presentable", right? | |
| Nov 9, 2009 at 0:22 | history | edited | Charles Rezk | CC BY-SA 2.5 |
typo
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| Nov 9, 2009 at 0:15 | history | answered | Charles Rezk | CC BY-SA 2.5 |