Timeline for functors $\text{Vect} \to \text{Vect}$ that preserve filtered and sifted colimits
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 29 at 8:56 | comment | added | Yang | @MartinBrandenburg, is this true for modules over a commutative ring? By the way, I see that the functors mentioned here not include the symmetric power, which didn't preserve even finite colimit as shown in this answer. | |
| Jan 30, 2020 at 1:42 | vote | accept | Dan Christensen | ||
| Jan 28, 2020 at 14:06 | comment | added | Dan Christensen | @JiříRosický That proposition exactly handles the remaining part of my question. Thanks! For others reading along, the cited paper is "Strongly complete logics for coalgebras" by A. Kurz and J. Rosický. | |
| Jan 28, 2020 at 14:05 | comment | added | Dan Christensen | @MartinBrandenburg I added the reference-request tag. Thanks for pointing it out. | |
| Jan 28, 2020 at 14:04 | history | edited | Dan Christensen |
Added reference-request tag
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| Jan 28, 2020 at 13:38 | comment | added | Jiří Rosický | Following 3.3 in arxiv.org/pdf/1207.2732.pdf, any functor ${\bf Vect}\to{\bf Vect}$ preserving filtered colimits preserves sifted colimits. | |
| Jan 28, 2020 at 10:07 | comment | added | Martin Brandenburg | Since you are looking for references, maybe the reference-tag would be suitable. I also know that these facts are true, but always wonder about references ... | |
| Jan 28, 2020 at 8:48 | comment | added | Ivan Di Liberti | In the case of sifted colimits, recall that by Thm. 3.1 in "What are Sifted Colimits?" by the usual suspects show that an endofunctor of a locally presentable category preserves sifted colimits iff it preserves directed colimits and reflexive coequalizers. | |
| Jan 28, 2020 at 2:25 | answer | added | Dylan Wilson | timeline score: 9 | |
| Jan 28, 2020 at 0:20 | comment | added | Dan Christensen | @IvanDiLiberti Thanks, those (recent!) theorems do give a straightforward way to check that the functors on my list preserve filtered colimits. I'd still be interested in a proof that requires less technology, and in whether those functors also preserve sifted colimits. | |
| Jan 27, 2020 at 22:40 | comment | added | Ivan Di Liberti | Thm. 3.12 and 3.13 in the abovementioned paper apply to your situation, as explained in 3.19. Also, the criterion of boundedness is extremely easy to check in your case. | |
| Jan 27, 2020 at 22:29 | comment | added | Ivan Di Liberti | I suggest to try and apply the equivalent characterizations of finitary functors provided by Adamek et al. in "On finitary functors": tac.mta.ca/tac/volumes/34/35/34-35abs.html. | |
| Jan 27, 2020 at 22:18 | history | asked | Dan Christensen | CC BY-SA 4.0 |