Timeline for Straightening for $\infty$-operads
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 15 at 21:30 | vote | accept | Jonathan Beardsley | ||
| May 15 at 21:30 | answer | added | Jonathan Beardsley | timeline score: 2 | |
| Jan 6, 2015 at 17:07 | comment | added | Jonathan Beardsley | @RuneHaugseng I wasn't really doing anything too serious. Just trying to see what it might look like to think about arxiv.org/abs/1102.1234 in terms of $\infty$-categories. | |
| Jan 5, 2015 at 17:40 | comment | added | Rune Haugseng | I think that's just a different construction (though related). Certainly you can define the composition product on symmetric sequences in any reasonably nice ordinary symmetric monoidal category (including, say, sets). There's a definition on the nlab that I imagine one could make sense of for $\infty$-categories too... What were you thinking of using this construction for? | |
| Jan 5, 2015 at 15:58 | comment | added | Jonathan Beardsley | @RuneHaugseng Lurie seems to imply that stability of the categories is really essential to getting the composition product of symmetric sequences to work. Do you know about this? | |
| Jan 5, 2015 at 13:29 | comment | added | Rune Haugseng | For a fixed set of objects, $\infty$-operads should presumably be the associative algebras in "coloured symmetric sequences" in spaces. As far as I know the monoidal $\infty$-category required for this to make sense has not been constructed, though. | |
| Jan 5, 2015 at 9:22 | comment | added | Fernando Muro | I think that infinity operads are Quillen equivalent to colored operads of simplicial sets. Does this maybe help? | |
| Jan 5, 2015 at 5:19 | comment | added | Jonathan Beardsley | But that seems to depend on stability and presentability. | |
| Jan 5, 2015 at 5:15 | comment | added | Jonathan Beardsley | It seems that, in light of section 6.3 of Lurie's Higher Algebra, we can think of $\infty$-operads as monoid objects in symmetric sequences on a symmetric monoidal category? | |
| Jan 5, 2015 at 4:10 | history | asked | Jonathan Beardsley | CC BY-SA 3.0 |