Timeline for A concrete example of the deficiency of triangulated categories?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 11, 2019 at 6:52 | vote | accept | Kim | ||
| Nov 3, 2019 at 20:00 | comment | added | Denis Nardin | @Kim I don't know off the top of my head (most applications coming to mind are homotopy theoretic in nature :)), but possibly a natural example is the study of algebraic K-theory. If I knew a nice ∞-categorical presentation of the Thomason-Troubaugh proof of Nisnevich descent I would definitely recommend it, only I don't think I know one... | |
| Nov 3, 2019 at 17:45 | comment | added | Kim | Would you happen to know a good written source where I can see stable $\infty$-categories being used (ideally to prove something interesting outside of the internal theory)? I think it would be helpful just to see standard manipulations and arguments with them. A setting that would be interesting to me would be derived categories of (any kind of) sheaves on schemes. | |
| Nov 3, 2019 at 16:44 | comment | added | Denis Nardin | @Kim I find stable ∞-categories easier in pretty much any context, but I am of course biased by my own point of view here. Really, setting up the theory of ∞-categories requires some work, but after it's done you can work with them quite transparently. I'm not overly expert on perverse sheaves or Poincaré duality so I don't feel confident talking about them, but I've been told that stable ∞-categories have some advantages if you want to do surgery theory, for example. | |
| Nov 3, 2019 at 16:30 | comment | added | Kim | Thank you, these are really informative answers! Would you happen to know if there are any drawbacks of triangulated categories for perverse sheaves or Poincare duality in that setting? Are stable $\infty$-categories any harder to work with (in terms of bookkeeping) than triangulated categories (for derived categories, say)? | |
| Nov 3, 2019 at 11:21 | history | edited | Denis Nardin | CC BY-SA 4.0 |
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| Nov 3, 2019 at 9:00 | history | edited | Denis Nardin | CC BY-SA 4.0 |
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| Nov 3, 2019 at 7:47 | history | edited | Denis Nardin | CC BY-SA 4.0 |
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| Nov 3, 2019 at 7:41 | history | answered | Denis Nardin | CC BY-SA 4.0 |