Timeline for Replacing triangulated categories with something better
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 27, 2019 at 21:37 | vote | accept | Hugh Thomas | ||
| Oct 20, 2019 at 16:56 | comment | added | Denis Nardin | @skd Yes! And I did not want to enter in the details, but it's ridiculously easy to check if an ∞-category is stable. It suffices to see that it has finite limits and that the functor $hΩ:hC→hC$ is an equivalence at the level of homotopy categories (this is because a left-exact functor of ∞-categories with finite limits is an equivalence iff it induces an equivalence on the homotopy category). Although, to be fair, usually it's not harder to prove that $Ω:C→C$ is an equivalence directly. | |
| Oct 20, 2019 at 16:41 | comment | added | skd | Another important point is that stability is a property of oo-categories, and not additional data. That's not true of triangulated categories. | |
| Oct 20, 2019 at 16:11 | comment | added | Patriot | "My opinion, and that of many other people although not of everyone, is..." Speaking as someone who belongs to the many other people you mentioned, I would be curious to hear the opinion of someone who disagrees. | |
| Oct 20, 2019 at 15:39 | history | edited | Denis Nardin | CC BY-SA 4.0 |
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| Oct 20, 2019 at 15:09 | history | edited | Denis Nardin | CC BY-SA 4.0 |
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| Oct 20, 2019 at 14:56 | history | answered | Denis Nardin | CC BY-SA 4.0 |