Timeline for endomorphisms of modules over symmetric ring spectra
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 1, 2014 at 9:59 | comment | added | Ulrich Pennig | So, if $N$ and $M$ are fibrant-cofibrant, then $End_R(N)$ is stably equivalent to $End_R(M)$ as symmetric spectra. Are they also equivalent as ring spectra? | |
| Jul 3, 2014 at 7:37 | vote | accept | Ulrich Pennig | ||
| Jul 3, 2014 at 5:01 | answer | added | Tyler Lawson | timeline score: 7 | |
| Jul 2, 2014 at 22:28 | comment | added | Fernando Muro | As @Fedotov suggests, derived mapping objects are homotopy invariant in any enriched model category, that means that mapping objects of fibrant-cofibrant objects are invariant. You can otherwise construct counterexamples, e.g. in chain complexes over a ring, the plain endomorphism ring of a module is concentrated in degree 0, while the derived endomorphism DGA has (in general) nontrivial higher homology: the Ext algebra. | |
| Jul 2, 2014 at 19:02 | comment | added | Ilias A. | If N and M are fibrant-cofibrant R-Modules then the answer is yes. | |
| Jul 2, 2014 at 17:45 | history | asked | Ulrich Pennig | CC BY-SA 3.0 |