Timeline for What is the symmetric monoidal structure on the $(\infty,1)$-category of spectra?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Dec 29, 2017 at 17:25 | comment | added | Denis Nardin | @RuneHagseng I'll confess I haven't checked all details, but I think you can use the category $I$ where the objects are the natural numbers $0,1,\dots$ and $\mathrm{Map}(i,j)=S^{j-i}$ (or empty if $i>j$) and composition is given by the collapse on the top cell $S^{j-i}\times S^{k-j}\to S^{k-i}$. Of course when you localize you'll also have to specify that the map $S^{j-i}\times X_i\to X_j$ restricts to the constant one on $S^{j-i}\vee X_i$. | |
| Dec 29, 2017 at 17:03 | comment | added | Rune Haugseng | That seems plausible, but what indexing category do you use? I guess you could replace finite spaces by finite sets and get something like an $\infty$-version of symmetric spectra, but can you literally recover this definition? | |
| Dec 29, 2017 at 11:53 | comment | added | Denis Nardin | Of course this is secretly the localized Day convolution again (with a different indexing category) | |
| Dec 29, 2017 at 11:05 | history | answered | Rune Haugseng | CC BY-SA 3.0 |