Timeline for Showing a functorial isomorphism
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 17, 2014 at 14:06 | comment | added | Samantha Y | Cool. Thank you very much for the help. I'm shocked I haven't seen that Theorem in Rotman. I guess I haven't spent as much time that far along the table of contents... | |
| Mar 17, 2014 at 9:29 | comment | added | Dag Oskar Madsen | If you know 2 out of 3 of the Auslander-Reiten formula, the Ext-Tor-isomorphism, and the isomorphism in this question, you can always prove the third. | |
| Mar 17, 2014 at 9:23 | comment | added | Dag Oskar Madsen | In the edition I have of Rotman, An introduction to homological algebra the Ext-Tor-isomorphism is Theorem 9.51. Keep in mind that $k$ is an injective $k$-module. | |
| Mar 17, 2014 at 1:15 | comment | added | Samantha Y | Interestingly, I checked a paper by Auslander, Representation theory of artin algebras III Almost Split Sequences and he shows directly that $\underline{Hom}(M, - ) \cong Tor_1(Tr M, -)$ | |
| Mar 16, 2014 at 21:59 | comment | added | Samantha Y | Do you have a reference for the proof of the isomorphism involving Ext and Tor? | |
| Mar 16, 2014 at 19:54 | comment | added | Dag Oskar Madsen | We can let $X=\operatorname{Tr} M$. That part could have been formulated better. | |
| Mar 16, 2014 at 16:57 | vote | accept | Samantha Y | ||
| Mar 16, 2014 at 16:50 | history | answered | Dag Oskar Madsen | CC BY-SA 3.0 |