Timeline for "Sums-compact" objects = f.g. objects in categories of modules?
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Jun 6, 2021 at 10:43 | comment | added | Sasha | @DavidWhite with some delay, I showed up to accept it :) | |
| Jun 6, 2021 at 10:42 | vote | accept | Sasha | ||
| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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| Nov 29, 2011 at 10:08 | history | edited | Pierre-Yves Gaillard | CC BY-SA 3.0 |
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| Nov 26, 2011 at 6:51 | history | edited | Pierre-Yves Gaillard | CC BY-SA 3.0 |
rewrote edit 4
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| Nov 25, 2011 at 12:42 | history | edited | Pierre-Yves Gaillard | CC BY-SA 3.0 |
typo
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| Nov 24, 2011 at 11:37 | history | edited | Pierre-Yves Gaillard | CC BY-SA 3.0 |
edit clearly indicated
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| Nov 23, 2011 at 6:04 | comment | added | Pierre-Yves Gaillard | Dear @Todd: I agree with you, especially with the "including proofs". I hope you will write something up for the nLab. If you do, thank you in advance for letting us know. | |
| Nov 22, 2011 at 21:23 | comment | added | Todd Trimble | Yes, please do share your thoughts, David. I'm following this discussion and would be very interested in collecting information (including proofs), so that I can write something up for the nLab. (Of course, anyone can get involved with the nLab.) | |
| Nov 22, 2011 at 14:37 | comment | added | Pierre-Yves Gaillard | Dear @David: Thank you very much for your kind comments! You seem to have a lot to say about this. I hope you'll post an answer of your own in a not too distant future. I appreciate all the comments you've made so far in this thread. | |
| Nov 22, 2011 at 14:22 | comment | added | David White | An example for (c) is in the linked paper: Lemma 1.2 and the remark afterwards that one of the inclusions is strict. The key observation seems to be that if you take the union of a strictly increasing $\kappa$-chain of sumpact modules (a.k.a. dually slender), then this is also sumpact. An example is the union of $\kappa$ many cyclic submodules. If $\kappa$ is uncountable then this module clearly is not finitely generated. I looked in T.Y.Lam's Lectures on Modules and Rings for a simpler example, but it's not there. Still, the example above is not so bad, & any example will need set theory | |
| Nov 22, 2011 at 14:04 | comment | added | David White | +1: This is a great answer. I've been wondering about this sumpact problem for a while, and I'm glad to see it settled. I hope Sasha shows up to accept this; it completely answers what he wanted. I'll see if I can figure out an example to answer (c). I suppose it's worth noting (from the OP's original question) that (a) and (b) are equivalent if $R$ is perfect, which is pretty cool | |
| Nov 22, 2011 at 6:43 | history | edited | Pierre-Yves Gaillard | CC BY-SA 3.0 |
edit clearly indicated
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| Nov 20, 2011 at 11:24 | history | edited | Pierre-Yves Gaillard | CC BY-SA 3.0 |
edit clearly indicated
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| Nov 19, 2011 at 11:32 | history | answered | Pierre-Yves Gaillard | CC BY-SA 3.0 |