Timeline for Transporting monoidal structure along adjunction
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 20 at 7:57 | answer | added | varkor | timeline score: 1 | |
| Aug 15, 2022 at 9:59 | comment | added | Maxime Ramzi | @W.Rether I guess that would be 4.1.7.4. for localizations + the fact that an adjunction in which the right adjoint is fully faithful is a localization, and maybe you would also benefit from 7.3.2.7. after having 4.1.7.4 | |
| Aug 13, 2022 at 15:43 | comment | added | W.Rether | Thanks! In case you come out with a more specific reference in Lurie please let me know! | |
| Aug 13, 2022 at 15:27 | comment | added | Maxime Ramzi | @W.Rether : I'm not sure, it seems like there is Brian Day's "Note on monoidal localizations", and there is also something in Lurie's Higher Algebra in the context of $\infty$-categories | |
| Aug 13, 2022 at 15:07 | comment | added | W.Rether | @MaximeRamzi could you provide a reference for the criterion posted in the first comment (when R is fully faithful)? Thanks! | |
| May 1, 2022 at 10:49 | comment | added | Maxime Ramzi | I'm not sure, but if $R$ is faithful then maybe your adjunction is monadic, or close to being so. For monadic adjunctions, there are some things you can say if the monad is strong, which should translate to some conditions on the adjunction. You could imagine a situation similar to Sets and abelian groups | |
| Apr 30, 2022 at 8:43 | comment | added | fyo | @MaximeRamzi , for my applications fully faithful is too much, but faithful should be ok. I have an impression that there should be a general theory for answering such questions, which I'm just not aware about. | |
| Apr 30, 2022 at 7:48 | comment | added | Maxime Ramzi | if $R$ is fully faithful equivalently, $L$ is a localization, or the co-unit $LR\to id$ is an isomorphism), and you have the following condition: "if $L(x\to y)$ is an isomorphism, then so is $L(x\otimes z\to y\otimes z)$ for all $z$", then you can do it. Is that the type of condition you're looking for ? Or are you also trying to get away from the fully faithful case | |
| S Apr 30, 2022 at 7:43 | review | First questions | |||
| Apr 30, 2022 at 8:09 | |||||
| S Apr 30, 2022 at 7:43 | history | asked | fyo | CC BY-SA 4.0 |