Timeline for Monomorphisms in functor categories
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| Jan 10, 2011 at 14:40 | comment | added | Theo Buehler | The point Sergio is making in his answer is a very good one -- it concerns your initial motivation that you want to show that filtered colimits of $R$-modules are exact. This is a special property of module categories and it is important to notice that the dual is wrong. Filtered limits of short exact sequences need not be exact, see en.wikipedia.org/wiki/Mittag-Leffler_condition | |
| Jan 10, 2011 at 14:04 | answer | added | Buschi Sergio | timeline score: 4 | |
| Jan 10, 2011 at 13:53 | answer | added | Finn Lawler | timeline score: 2 | |
| Jan 10, 2011 at 13:52 | answer | added | Martin Brandenburg | timeline score: 2 | |
| Jan 10, 2011 at 13:34 | comment | added | Łukasz Grabowski | @Ralph: To show that mono implies (*) at a given i \in I consider a system over I which is non-zero only at i. | |
| Jan 10, 2011 at 13:18 | comment | added | Ralph | @Lukasz: Thanks for the reference. But they also take (*) as definition for being mono. | |
| Jan 10, 2011 at 13:03 | comment | added | Łukasz Grabowski | Showing that taking direct limit is exact is exercise 19 in chapter 2 of Atiyah-Macdonald (there's a hint there). | |
| Jan 10, 2011 at 12:56 | history | edited | Ralph | CC BY-SA 2.5 |
deleted 10 characters in body
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| Jan 10, 2011 at 12:46 | history | asked | Ralph | CC BY-SA 2.5 |