Timeline for When are projective modules closed under highly-filtered colimits?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 19, 2022 at 13:29 | comment | added | Tim Campion | @SeanCox Oh wow, that's really cool! Thanks for sharing! This is relevant to another MO question I once asked too. | |
| Jan 19, 2022 at 13:05 | comment | added | Sean Cox | @TimCampion The assertion that "every small projectivity class in an accessible category is accessibly embedded" follows from Vopěnka's Principle (and is independent of ZFC). See our new preprint: <arxiv.org/abs/2201.06782> | |
| Feb 26, 2020 at 2:30 | vote | accept | Tim Campion | ||
| Feb 24, 2020 at 21:59 | comment | added | Leonid Positselski | No, concerning (1), this is just a new (and very interesting) result which I happen to have heard about. I am not an expert on such things, have not studied the details, and do not know what the potential for generalizations of this theorem may be. | |
| Feb 24, 2020 at 20:01 | comment | added | Tim Campion | Actually, your (1) is stronger than I expected might be known. Do you know whether large cardinal hypotheses imply more generally that every small-projectivity class in a locally presentable category is accessibly embedded -- or perhaps even that the left half of an accessible wfs is accessibly embedded in the arrow category? | |
| Feb 24, 2020 at 19:54 | comment | added | Tim Campion | Thanks, this is fantastic! I will hold off for a bit on accepting in hopes of hearing about more ZFC examples and about negative results under anti-large-cardinal hypotheses, and about more precise consistency-strength calibrations, but I think this is primarily what I was looking for. | |
| Feb 24, 2020 at 19:46 | history | answered | Leonid Positselski | CC BY-SA 4.0 |