Timeline for If a $\otimes$-idempotent object has a dual, must it be self-dual?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Aug 19, 2017 at 15:56 | answer | added | Tim Campion | timeline score: 1 | |
| Aug 16, 2017 at 23:58 | comment | added | Tim Campion | I just found a preprint of Boyarchenko and Drinfeld which studies "well-idempotent" and "co-well-idempotent" objects. Their terminology is "closed idempotent" and "open idempotent". | |
| Aug 10, 2017 at 16:24 | comment | added | Mike Shulman | You're very polite, but of course my "answer" was not really an answer to the question as you asked it. It's intriguing that while the answer to question 1 is "no" in both symmetric and non-symmetric contexts, the answer to question 2 is "yes" in the symmetric context but "no" in the non-symmetric one. I wonder what the answer to question 3 is in the non-symmetric context. | |
| Aug 9, 2017 at 16:15 | comment | added | Tim Campion | I've accepted MTyson's answer, although of course the complete answer to my question also involves Anton Fetisov's answer, or Will Sawin's simplification. Mike Shulman's answer also provides important context! | |
| Aug 9, 2017 at 16:14 | vote | accept | Tim Campion | ||
| Aug 9, 2017 at 12:16 | answer | added | Will Sawin | timeline score: 3 | |
| Aug 9, 2017 at 0:47 | comment | added | Tim Campion | Following Anton's example below, note that if $C$ is a self-dual category (i.e. equivalent to its opposite), then $C^\mathbb{N}$ is self-dual and idempotent in $Dist$, but it is typically not well-idempotent, -- e.g. if $C$ is finite sets and bijections. So this whole business was not as sharp as I thought it was -- well-idempotency is stronger than idempotency + self-duality. I'm not sure what the "right" notion of "self dual idempotent object" is, but being well-idempotent might be a reasonable guess. Perhaps there's additional coherences to be had, though. | |
| Aug 9, 2017 at 0:39 | history | edited | Tim Campion | CC BY-SA 3.0 |
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| Aug 9, 2017 at 0:28 | answer | added | Anton Fetisov | timeline score: 4 | |
| Aug 8, 2017 at 21:07 | vote | accept | Tim Campion | ||
| Aug 8, 2017 at 21:10 | |||||
| Aug 7, 2017 at 23:09 | answer | added | MTyson | timeline score: 6 | |
| Aug 7, 2017 at 10:24 | answer | added | Mike Shulman | timeline score: 12 | |
| Aug 4, 2017 at 21:32 | history | edited | Tim Campion | CC BY-SA 3.0 |
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| Aug 4, 2017 at 21:27 | history | asked | Tim Campion | CC BY-SA 3.0 |