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 2, 2014 at 5:43 | comment | added | Tyler Lawson | @UlrichPennig Neither $Hom_R(M,N)$ nor $Hom_R(N,M)$ has a strictly associative ring structure, and one of these is always the source or target of such a composition operation. As a result, to construct an equivalence between $End_R(M)$ and $End_R(N)$ you really do need a third object with a ring structure to move between them, as in the third paragraph. (If you allow yourself to talk about $A_\infty$ algebras instead, the answer to your question is "yes".) However, if you just work in the derived category, then yes: all four admit ring spectrum structures compatible with $\phi$. | |
| Aug 1, 2014 at 10:04 | comment | added | Ulrich Pennig | If pre- and postcomposition with $\phi$ are weak equivalences, then the endomorphism spectra are equivalent as (symmetric) spectra. Are they also equivalent as ring spectra? | |
| Jul 3, 2014 at 11:56 | comment | added | Ulrich Pennig | Considering my last comment, it actually sounded quite negative. Actually, I am looking forward to learning more about model categories :-). | |
| Jul 3, 2014 at 7:37 | vote | accept | Ulrich Pennig | ||
| Jul 3, 2014 at 7:37 | comment | added | Ulrich Pennig | Geez, I need to learn more model category theory. Thank you! | |
| Jul 3, 2014 at 5:01 | history | answered | Tyler Lawson | CC BY-SA 3.0 |