Timeline for Extension problem
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 29, 2010 at 13:33 | answer | added | Chris Schommer-Pries | timeline score: 7 | |
| Jul 29, 2010 at 13:30 | vote | accept | ashpool | ||
| Jul 29, 2010 at 13:25 | comment | added | darij grinberg | Since this seems to be your point of confusion, I should add that the elements of $\mathrm{Ext}^1\left(B,A\right)$ are the isomorphism classes of EXACT SEQUENCES $0\to A\to X\to B\to 0$ and not just the isomorphism classes of those $X$ for which such exact sequences exist. An exact sequence $0\to A\to X\to B\to 0$ is not uniquely defined by $A$, $X$ and $B$; we also need to know the maps! For instance, in your case, there are four different exact sequences $0\to \mathbb Z\to\mathbb Z\to \mathbb Z\diagup\left(3\right)\to 0$, and they are isomorphic in pairs, but not all isomorphic to each other | |
| Jul 29, 2010 at 13:21 | answer | added | Graham Leuschke | timeline score: 8 | |
| Jul 29, 2010 at 13:19 | comment | added | darij grinberg | The isomorphisms should commute with the injection $A\to X$ and the surjection $X\to B$. This leaves less freedom for the isomorphisms, and thus we get more distinct $X$'es. | |
| Jul 29, 2010 at 13:16 | history | edited | ashpool | CC BY-SA 2.5 |
added 74 characters in body; added 13 characters in body
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| Jul 29, 2010 at 13:01 | history | asked | ashpool | CC BY-SA 2.5 |