Timeline for 2-categories for the working algebraic geometer
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| Dec 9, 2022 at 8:52 | vote | accept | Gabriel | ||
| Dec 8, 2022 at 16:11 | answer | added | David White | timeline score: 5 | |
| S Nov 24, 2022 at 12:01 | history | bounty ended | CommunityBot | ||
| S Nov 24, 2022 at 12:01 | history | notice removed | CommunityBot | ||
| Nov 16, 2022 at 17:25 | comment | added | Gabriel | Dear Martin and Tim, due to Denis Nardin's comment, my question is about (2,1)-categories. (The first reference seems to go deep into the intricacies of bicategories, and it's not really "quick". The second one is also not about (2,1)-categories.) | |
| Nov 16, 2022 at 13:54 | comment | added | Tim Campion | Gaitsgory and Rozenblyum's A Study in Derived Algebraic Geometry Volume I and Volume II is a pioneering work which embraces $(\infty,2)$-categorical methods. But I'm sure Denis Nardin is right that the specific examples of statements you give might not be the places where this is most crucial. | |
| Nov 16, 2022 at 12:52 | comment | added | Martin Brandenburg | To be honest I think the question is too broad and vague. Or is this just about the two examples? In any case, have a look at this book: arxiv.org/abs/2002.06055 It is a really good intro to 2-categories. | |
| Nov 16, 2022 at 11:04 | history | edited | Martin Sleziak |
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| S Nov 16, 2022 at 10:58 | history | bounty started | Gabriel | ||
| S Nov 16, 2022 at 10:58 | history | notice added | Gabriel | Draw attention | |
| Apr 1, 2022 at 8:58 | history | edited | Gabriel | CC BY-SA 4.0 |
added 11 characters in body
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| Apr 1, 2022 at 8:58 | comment | added | Gabriel | Oh, that was absolutely a typo! Thanks for noticing! | |
| Apr 1, 2022 at 8:51 | comment | added | Donu Arapura | @Gabriel Perhaps you meant to write "...the derived category of $\overline{\mathbb{Q}}_\ell$-sheaves...". As for the subtlety, see Ekedahl's paper The adic formalism. | |
| Apr 1, 2022 at 6:09 | comment | added | Gabriel | @DonuArapura perhaps! Would you mind explaining a bit further? | |
| Mar 31, 2022 at 21:30 | comment | added | Donu Arapura | I'm not sure you wrote what you meant to write for example 1. That example is pretty subtle though | |
| Mar 31, 2022 at 18:17 | comment | added | Denis Nardin | For everything you mentioned here (2,1)-categories are sufficient (where basically none of the subtleties of 2-category theory apply). In fact (∞,1)-category theory is much simpler than even 2-category theory... | |
| Mar 31, 2022 at 17:32 | comment | added | Wojowu | If you ever find yourself thinking about stacks, you will encounter a fair bit of 2-category theory. I think some introductions to stacks might cover some of the relevant background. | |
| Mar 31, 2022 at 17:26 | history | asked | Gabriel | CC BY-SA 4.0 |