Timeline for Higher coherent multiplicative structures on S-algebras
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 11, 2014 at 20:11 | comment | added | Geoffroy Horel | Let us continue this discussion in chat. | |
| Sep 11, 2014 at 20:09 | comment | added | Geoffroy Horel | Well, this is more or less worked out in geoffroy.horel.org/Operads,%20modules%20and%20TFT.pdf | |
| Sep 11, 2014 at 20:05 | vote | accept | Jonathan Beardsley | ||
| Sep 11, 2014 at 20:05 | comment | added | Jonathan Beardsley | I see. Ah, that's frustrating. I mean, yeah, I'm interested entirely in $E_2$ and above, but I guess I was hoping this had been worked out. Thanks! | |
| Sep 11, 2014 at 20:03 | comment | added | Geoffroy Horel | Then the first problem is to construct the tensor product. You want to send $(M,N)$ to $M\otimes_AN$. This does not even make sense since $M$ is not a right $A$-module. If A is at least $E_2$, then $A$ and $A^{op}$ are equivalent and it is not too hard to construct the monoidal structure in the homotopy category. But there is a lot of technicality needed to construct a good point set-level construction of this tensor product. | |
| Sep 11, 2014 at 19:58 | comment | added | Jonathan Beardsley | Nah I'm just talking about an $A$-module in the traditional sense. | |
| Sep 11, 2014 at 19:56 | comment | added | Geoffroy Horel | There are (at least) two reasonable definitions of a module over an E_n-algebra. I assumed that you meant module over the underlying associative algebra but maybe you meant module in the operadic sense. In both cases, constructing the monoidal structure is a bit tricky. | |
| Sep 11, 2014 at 19:45 | comment | added | Jonathan Beardsley | So it's not clear that one can actually tensor together two $A$-modules and get another $A$-module back, is that what you're saying? | |
| Sep 11, 2014 at 18:15 | history | answered | Geoffroy Horel | CC BY-SA 3.0 |