Timeline for Is there a "relative version" of the theorem that every locally presentable category has all small limits?
Current License: CC BY-SA 4.0
5 events
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| Nov 6, 2022 at 16:59 | comment | added | Tim Campion | @MartinBrandenburg You may be right in the end (and I did mention this possibility in my second bullet above -- but you're right to point out that SAFT is directly used in the proof of Theorem 1, making this perspective all the more compelling). Maybe it's a linguistic trap to say "well, this is a statement about limit existence; its 'relative version' should say something about limit-preservation" | |
| Nov 6, 2022 at 16:56 | comment | added | Tim Campion | @IvanDiLiberti I had not seen that, thanks! That result sounds like maybe the strongest thing I could imagine being true along these lines, so it's probably the best answer I could hope for... unless there's some sort of simplification if $F$ is assumed to preserve colimits or something like that... | |
| Nov 5, 2022 at 23:18 | comment | added | Martin Brandenburg | I wonder why the relative version should be about preservation of limits? The existence of limits (of a given shape) is a special case of a right adjoint functor. So the existence of right adjoints would be more natural, right? | |
| Nov 5, 2022 at 19:00 | comment | added | Ivan Di Liberti | Have you seen this: arxiv.org/abs/2110.14192? | |
| Nov 5, 2022 at 18:31 | history | asked | Tim Campion | CC BY-SA 4.0 |