Timeline for When do chain complexes decompose as a direct sum?
Current License: CC BY-SA 2.5
5 events
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| Jul 25, 2010 at 0:48 | comment | added | Tom Goodwillie | I meant to say it started with Sullivan's rational homotopy. | |
| Jul 22, 2010 at 11:54 | comment | added | Tom Goodwillie | Certainly "formal" is used to mean "weakly equivalent to its homology" in various contexts where the chain complexes and their homology have some ring, co-ring, .... structure. It started with Quillen's rational homotopy and happily spread, and no doubt is used for chain complexes of $R$-modules these days. "Hereditary": now that you say it, I have seen that definition, but if you had said to me out of context "suppose $R$ is a hereditary ring" I would not have known what you meant. | |
| Jul 22, 2010 at 7:18 | comment | added | Victor Protsak | I endorse the opening lament! Tom, isn't "quasi-isomorphic to its homology" known as "formal" and the ring such that submodules of projectives are projective ... "hereditary"? | |
| Jul 22, 2010 at 1:53 | history | edited | Tom Goodwillie | CC BY-SA 2.5 |
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| Jul 22, 2010 at 0:52 | history | answered | Tom Goodwillie | CC BY-SA 2.5 |