Timeline for Are there universe-indexed spectra over simplicial sets?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Jan 23, 2010 at 15:56 | vote | accept | user2146 | ||
| Jan 22, 2010 at 19:33 | comment | added | Chris Schommer-Pries | Ahh I see. If you really must work with EKMM, then you need to do a two stage comparison. (1) Go from EKMM spectra to orthogonal spectra: sequences of spaces indexed on inner product spaces together with structure maps, $S^V \wedge E(W) \to E( V \oplus W)$. There is no (overt) operad in the game though. Then you want to pass to the simplicial version of orthogonal spectra: simplicial sets indexed by inner product spaces together with maps like the above, but where $S^V$ is the singular simp. set, as you guessed. I believe both of these transitions are explained in the paper I cited. | |
| Jan 22, 2010 at 14:29 | comment | added | user2146 | Thanks! This is already partially helpful, but Tyler is right. As far as I see EKMM work with topological spaces only and I wonder how to handle the $S^V$ in the definition of structure maps, if I try to use simplicial sets and no topological spaces. | |
| Jan 22, 2010 at 13:35 | comment | added | Tyler Lawson | I think one issue the original poster referred to with "universe-indexed" spectra is that in, say, the EKMM definition one has structure maps $S^V \wedge E(W) \to E(V \oplus W)$ for any orthogonal pair of subspaces of $\mathcal U$. The lack of simplicial structure on $S^V$ obstructs writing down a direct analogue. | |
| Jan 22, 2010 at 12:20 | history | answered | Chris Schommer-Pries | CC BY-SA 2.5 |