Timeline for Comparing $\mathcal C$ and $\mathcal C^{\mathcal C}$ (where $\mathcal C$ is a category)
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 28, 2019 at 22:58 | vote | accept | Pierre-Yves Gaillard | ||
| Jun 27, 2019 at 15:35 | history | edited | Pierre-Yves Gaillard | CC BY-SA 4.0 |
edit clearly indicated
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| Jun 27, 2019 at 15:25 | comment | added | Pierre-Yves Gaillard | @EmilJeřábek - Yes, you're perfectly right! I'll edit. Thank you very much! | |
| Jun 27, 2019 at 15:13 | comment | added | Emil Jeřábek | You just gave a negative answer, but as far as I can tell, this does not resolve the linked question on poset isomorphic to their endomorphism posets. (The endomorphism poset of $\mathbb R$ is very different from $\mathbb R$.) So I believe that claim in the question is faulty. | |
| Jun 27, 2019 at 14:45 | answer | added | Pierre-Yves Gaillard | timeline score: 5 | |
| Jun 25, 2019 at 13:39 | comment | added | Asaf Karagila♦ | @Tim: Of course, but it might just end up as one. | |
| Jun 25, 2019 at 13:38 | comment | added | Tim Campion | @AsafKaragila Yeah, I guess I was thinking "If we formalize this in ZFC + a universe rather than a class theory, then they're equivalent." But I didn't get the impression that the question is supposed to be about the subtelties of classes in ZFC. | |
| Jun 25, 2019 at 13:35 | comment | added | Asaf Karagila♦ | @Tim: Why do you think they are equivalent? (I'm not saying they are not, I just want to see if your logic is correct. To wit, it is consistent with ZFC that there is a class that surjects onto the ordinals, but there is no injection from the ordinals into it.) | |
| Jun 25, 2019 at 13:28 | comment | added | Tim Campion | If we're working in ZFC, then (1) and (2) are equivalent. For that matter, technically we need to be working in some sort of theory that allows us to talk about classes, anyway. | |
| Jun 25, 2019 at 12:49 | history | asked | Pierre-Yves Gaillard | CC BY-SA 4.0 |