Timeline for $A_\infty$ structure on Ext-algebras well defined?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 13, 2012 at 18:23 | vote | accept | Jan Weidner | ||
| Mar 12, 2012 at 22:47 | history | edited | David White | CC BY-SA 3.0 |
Fixed typo
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| Mar 12, 2012 at 19:12 | answer | added | Leonid Positselski | timeline score: 9 | |
| Mar 12, 2012 at 18:18 | comment | added | Fernando Muro | There's a very basic lemma on homological algebra which says that projective resolutions are essentially unique, in the sense that two of them are homotopy equivalent, therefore their endomorphism DG-algebras become homotopy equivalent too (through a zig-zag of equivalences, though). The same holds for injective resolutions by the same reason that $Ext$ can be computed both kinds of resolutions. | |
| Mar 12, 2012 at 18:04 | comment | added | MTS | Ah, I see. Thanks for the clarification. I don't know the answer, but it's an interesting question for sure. | |
| Mar 12, 2012 at 17:24 | comment | added | Jan Weidner | I guess one can do both. I mean the total complex of the double complex $Hom(P,P)$. On $Hom(P,M)$ the dg-algebra structure is not so obvious to me, thats why I have choosen $Hom(P,P)$. | |
| Mar 12, 2012 at 17:04 | comment | added | MTS | In the construction of the Ext-algebra, don't you form the Hom complex $Hom^\bullet (P,M)$ and then take homology? It seems like $Hom^\bullet (P,P)$ would be a double complex... | |
| Mar 12, 2012 at 16:39 | history | asked | Jan Weidner | CC BY-SA 3.0 |