Timeline for "Characteristics" (thick subcategories) in $n$-groupoids
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 17, 2017 at 19:32 | comment | added | Niles | One pointer to literature: the notion of "Picard category" (a.k.a. "Picard groupoid", a.k.a. "2-abelian group", etc. ) models 1-truncated connective spectra, and this may be a place where one can answer the question about thick subcategories. An initial guess: two cyclic groups of order p (objects and automorphisms) joined by a nontrivial symmetry (modeling the Postnikov invariant). | |
| Apr 17, 2017 at 19:25 | comment | added | Niles | This is a good question, with another good question inside of it! The subtle "inner question" is, I take it, whether there's some algebraic (categorical) notion of Abelian group object in n-categories which models n-truncated connective spectra in the way that Abelian groups model Eilenberg-Mac Lane spectra. This is a stable version of the Homotopy Hypothesis, and is something I've thought about (along with many others). The main, "outer", question is whether one can classify the thick subcategories in such a category, and this is one I haven't come across before but I think is wonderful! | |
| Apr 11, 2017 at 11:19 | comment | added | Sean Tilson | @QiaochuYuan Cool, do you have a reference? Are you also implicitly replacing n-groupoids with something else? | |
| Apr 10, 2017 at 23:39 | comment | added | Qiaochu Yuan | Yes, it should be spectra with homotopy groups in $[0, n]$. | |
| Apr 10, 2017 at 22:18 | history | asked | Yuri Sulyma | CC BY-SA 3.0 |