Timeline for Question regarding 2-mathematics: Can you stackify a 2-functor without prestackifying it first?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 11, 2014 at 16:34 | vote | accept | Modnar | ||
| Oct 11, 2014 at 15:17 | comment | added | S. Carnahan♦ | I think it should be fine, but I'm not a set theorist. | |
| Oct 11, 2014 at 15:16 | comment | added | Modnar | EDIT: Also since we are assuming that the associated stack already exists, would that difficulty still exists? | |
| Oct 11, 2014 at 15:15 | answer | added | S. Carnahan♦ | timeline score: 10 | |
| Oct 11, 2014 at 14:50 | comment | added | Modnar | What do you mean by foundations? Do you mean the site structure? If so, could we assume that for very good sites, this proposition would hold? | |
| Oct 11, 2014 at 13:45 | comment | added | S. Carnahan♦ | There is a set-theoretic problem that may appear if your foundations aren't chosen carefully. Waterhouse constructed a presheaf on affine schemes in the flat topology that has no sheafification. Unsurprisingly, the same problem happens in the stack world. | |
| Oct 11, 2014 at 13:17 | comment | added | Modnar | Hmm.. Thank you very much. So there is at least a 'high chance' that it works in 'good situations'. That is indeed good to know. Anyways, if anyone has an actual proof, it would be much appreciated if you could give a citation. Thanks again. | |
| Oct 11, 2014 at 12:52 | comment | added | Zhen Lin | This seems to be a folklore result. It is alluded to in [Higher topos theory, §6.5.3]. | |
| Oct 11, 2014 at 12:12 | history | edited | Modnar | CC BY-SA 3.0 |
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| Oct 11, 2014 at 12:05 | comment | added | Simon Henry | I don't Know, but I'm sure somebody will. Maybe you should consider editing your question if it is what you want to know ? | |
| Oct 11, 2014 at 11:53 | comment | added | Modnar | Thanks for the answer. But then, what about doing the descant data twice, or probably 3 times, i.e. defined $A''(U):=2$-$lim_{\mathfrak{U}}(Des(\mathfrak{U},A'))$ and then again $A'''$. Would that work? | |
| Oct 11, 2014 at 11:47 | comment | added | Simon Henry | This is already not working with sheaficiation: if you try to sheafify directl a non separated sheaf this does not neccearly gives a sheaf, but a separated presheaf and you have to go to the process twice to abtain the sheafification. | |
| Oct 11, 2014 at 10:17 | review | First posts | |||
| Oct 11, 2014 at 10:33 | |||||
| Oct 11, 2014 at 10:14 | history | asked | Modnar | CC BY-SA 3.0 |