Timeline for (Commutative) Algebras in $\mathsf{dgCat}_k$
Current License: CC BY-SA 4.0
7 events
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| Oct 20, 2022 at 23:01 | comment | added | AT0 | @Stahl I think this might be in the papers 'Spaces of operad structures' and 'The homotopy theory of simplicially enriched multicategories' , or it seems to match some of what Jon Pridham might be referencing. | |
| Oct 20, 2022 at 18:19 | comment | added | Stahl | Thank you both for the suggestions! @JonPridham, do you have any idea where I might access Marcy Robertson's thesis? I haven't been able to track it down. | |
| Oct 12, 2022 at 21:54 | comment | added | David White | I like Jon Pridham's suggestion. For some reason, names that jump into my head reading that are Elmendorf and also Niles Johnson and Donald Yau. Another option might be to weaken the model category axioms. If the issue has to do with the cofibrations and the monoidal product, then maybe a right semi-model structure would still have its notion of homotopy coherent monoidal product. Or one of Simon Henry's weak model structures (if he has a notion of what it means for one to be monoidal). Maybe focusing on only the Brown category of fibrant objects inside the model structure. Just brainstorming. | |
| Oct 12, 2022 at 19:42 | comment | added | Jon Pridham | For model structures, Marcy Robertson's 2008 thesis covers a lot of ground. There's also a paper by Stanculescu. I can't remember where I first read to use the embedding of monoidal categories in multicategories, it's so ingrained. | |
| Oct 12, 2022 at 18:14 | comment | added | Stahl | @JonPridham Thanks for this! Are there any "standard" places where one might learn the basics about these things and their homotopy theory, or any references where they're used to circumvent issues similar to the ones I mentioned in the question? | |
| Oct 12, 2022 at 8:46 | comment | added | Jon Pridham | The usual workaround for questions like this is to use the model category of (symmetric) dg multicategories, a.k.a. coloured dg operads. That forms a much larger category than monoidal dg categories, and that flexibility allows e.g. cofibrant replacement. | |
| Oct 12, 2022 at 5:45 | history | asked | Stahl | CC BY-SA 4.0 |