Timeline for Regularly well-powered iff regularly co-well-powered?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 15, 2021 at 1:55 | vote | accept | Tim Campion | ||
| Feb 13, 2021 at 20:29 | history | became hot network question | |||
| Feb 13, 2021 at 20:23 | comment | added | Tim Campion | Quick, someone throw Asaf a set theory question, the isolation is getting to him! | |
| Feb 13, 2021 at 20:16 | comment | added | Asaf Karagila♦ | @IvanDiLiberti: What are whiteboards? I forgot. | |
| Feb 13, 2021 at 14:28 | answer | added | Kevin Carlson | timeline score: 4 | |
| Feb 13, 2021 at 13:08 | comment | added | Ivan Di Liberti | On a conceptual level, I do see a pairing $<-,->: \mathsf{RSub} \times \mathsf{RQuo} \to 2$, then of course whether this is the correct pov, it's hard to tell. | |
| Feb 13, 2021 at 13:01 | comment | added | Ivan Di Liberti | That was my idea. It's hard to say without spending time on a whiteboard. | |
| Feb 13, 2021 at 13:00 | comment | added | Tim Campion | @IvanDiLiberti That sounds promising. The usual ways I know of relating subobjects and quotients -- taking kernels / cokernels, taking kernel pairs / quotienting by a congruence etc. seem to require stronger exactness properties than I'm assuming here. It would be interesting if there were something like this which didn't require any sort of exactness. | |
| Feb 13, 2021 at 12:59 | comment | added | Ivan Di Liberti | One way to think about this could be to study the presheaf $\mathsf{RSub}$ of regular subobject and the copresheaf $\mathsf{RQuo}$ of regular quotient. Now one could try to say that there must be an injective map $\mathsf{RQuo} \to 2^\mathsf{RSub}$ (notice that the variance now match). Similar tricks are used by Freyd in Sec 5 of "On the concreteness of certain categories", for very different purposes. | |
| Feb 13, 2021 at 12:51 | comment | added | Tim Campion | @AsafKaragila Exactly. Unfortuately, "co-well-powered" means that it's also connected to a continuous energy drain. So the above theorem that $(1) \Leftrightarrow (2)$ is really a weak form of the 0th law of thermodynamics. | |
| Feb 13, 2021 at 12:45 | comment | added | Asaf Karagila♦ | By well-powered do you mean "connected to a continuous energy source"? | |
| Feb 13, 2021 at 12:28 | history | asked | Tim Campion | CC BY-SA 4.0 |