Timeline for Dualizable object in the category of locally presentable categories
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 3, 2019 at 20:57 | history | edited | Simon Henry | CC BY-SA 4.0 |
deleted 7 characters in body
|
| Jul 3, 2019 at 20:51 | vote | accept | Simon Henry | ||
| Jul 3, 2019 at 20:51 | answer | added | Simon Henry | timeline score: 7 | |
| Jul 3, 2019 at 20:41 | comment | added | Ivan Di Liberti | Oh, thanks for this observation! | |
| Jul 3, 2019 at 20:35 | comment | added | Simon Henry | @IvanDiLiberti : Beware that topos theorist have used the term "dualizable" here for something that have very little to do with strong duality in monoidal categories. I do not think there are any connection between exponentiability of the topos T and its dualizability in the sense I'm talking about here. Though (and it connects with Dylan Wilson's comment and your second comments) it has been shown (cf arxiv.org/abs/1802.10425) that if a topos $T$ is exponentiable then the category of sheaves of spectra on it is dualizable in the category of stable locally presentable category. | |
| Jul 3, 2019 at 12:15 | comment | added | Ivan Di Liberti | Interesting! This is precisely the definition of continuous locally presentable category! | |
| Jul 3, 2019 at 11:17 | history | became hot network question | |||
| Jul 3, 2019 at 11:15 | comment | added | Dylan Wilson | The analogous question for presentable stable infty-categories and for R-linear infty-categories is studied in SAG.D.7. Lurie shows that you’re dualizable iff you’re also a retract of Ind(C_0) for some small C_0 where the retraction and section preserve filtered colimits. | |
| Jul 3, 2019 at 10:15 | answer | added | Yonatan Harpaz | timeline score: 14 | |
| Jul 3, 2019 at 5:01 | answer | added | Theo Johnson-Freyd | timeline score: 11 | |
| Jul 2, 2019 at 22:30 | comment | added | Ivan Di Liberti | Just an idea: Isn't the inclusion of topoi in locally presentable categories monoidal? If so dualizable topoi are dualizable locally presentable categories. To my understanding, dualizable topoi coincide with exponentiable topoi and those are topoi that are continuous categories. This leads to the conjecture that locally presentable continuous categories are dualizable in your setting. | |
| Jul 2, 2019 at 20:38 | history | asked | Simon Henry | CC BY-SA 4.0 |