Timeline for Mitchell's embedding theorem
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Sep 24, 2010 at 17:55 | answer | added | Dylan Wilson | timeline score: 1 | |
| Aug 20, 2010 at 14:01 | comment | added | Agustí Roig | @Theo. Glad to see that someone else needs the result. But I'm pessimistic too, after looking (although I must admit only superficially) to some of the proofs of the theorem: just at the beginning you seem always need the commutativity of limits and colimits, so products apparently must be finite. | |
| Aug 20, 2010 at 3:10 | comment | added | Theo Johnson-Freyd | This question has been dormant for a month, but I would like to mention that there are other reasons for wanting a stronger Mitchell. My own research would strongly like it to satisfy (a), at least. But I'm currently pessimistic. | |
| Jul 18, 2010 at 9:14 | comment | added | Martin Brandenburg | Everybody knows that you have a lot of experience. But this does not justify that below every question you don't like you guide the OP towards other more "relevant" questions or problems, without answering at all the actual question. This is also the reason why I won't post any question here anymore. As for my experience, I have tought several algebra-related courses and also dislike the affection of using Mitchell's theorem, but that's not the point at all here. Agusti's question is interesting in it's own right, it does not suggest to actually use the theorem anytime. | |
| Jul 17, 2010 at 20:10 | comment | added | BCnrd | @Martin, I'm offering advice based on experience (which you lack) and seeing students use Mitchell's theorem only to realize later that it doesn't help much, that's all. I also know a thing or two about useful ways to work with sheaf cohomology; the given motivation is not leading in a good direction for that. I don't see any big deal about offering precise advice based on experience in a comment box. I wrote "as far as I know" to make it clear that I am open to hearing examples to the contrary. I never wrote that I have an "important opinion"; don't put words in my mouth. Lighten up, dude. | |
| Jul 17, 2010 at 14:30 | comment | added | Martin Brandenburg | @BCnrd: And again, you don't adress the question, but just mention your important opinion about the subject ... @Agusti: I think you should give it a try. | |
| Jul 17, 2010 at 3:29 | comment | added | Agustí Roig | @Martin. Have you seen the proof? (For instance, in Borceux's book.) That's what I was trying NOT to do (at least, not before being sure that no one has already done it). :-) | |
| Jul 17, 2010 at 3:18 | comment | added | BCnrd | My advice (based on much experience) is to never ever use the Mitchell embedding theorem. It promotes not paying attention to what is going on, and I have never seen any situation anywhere for which this theorem is of much use anyway. Once you learn the trick of "chasing members" from MacLane's book "Categories for the working..." it ceases to have any purpose at all (as far as I know). Better off to acquire the skill of working in abelian categories by thinking functorially. I would be interested to see even one example where ignoring this fact really creates a problem. | |
| Jul 16, 2010 at 16:37 | comment | added | Martin Brandenburg | Interesting question. What happens when you go through the proof of the theorem and try to check the properties? | |
| Jul 16, 2010 at 14:04 | history | asked | Agustí Roig | CC BY-SA 2.5 |