Timeline for Is there a sense in which the homotopy theory of simplicial sets is the "paradigmatic" one?
Current License: CC BY-SA 4.0
12 events
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| Jul 28, 2022 at 8:22 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Jan 10, 2015 at 7:45 | answer | added | მამუკა ჯიბლაძე | timeline score: 8 | |
| Jul 18, 2012 at 11:04 | history | edited | Mirco A. Mannucci | CC BY-SA 3.0 |
edited title
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| Jul 18, 2012 at 9:58 | answer | added | Ronnie Brown | timeline score: 8 | |
| Jul 18, 2012 at 1:01 | answer | added | David Roberts♦ | timeline score: 7 | |
| Jul 17, 2012 at 19:52 | comment | added | Akhil Mathew | (Here $\infty$ should be $(\infty, 1)$.) | |
| Jul 17, 2012 at 19:51 | comment | added | Akhil Mathew | A restatement of Peter Arndt's answer: the "universal property" of the $\infty$-category ("homotopy theory") $\mathcal{S}$ of spaces (Kan complexes, etc.) is that, for any $\infty$-category $\mathcal{C}$ admitting all colimits, there is an equivalence of $\infty$-categories $\mathrm{Fun}^L(\mathcal{S}, \mathcal{C})) \simeq \mathcal{C}$ given by evaluation on a point ($L$ means colimit-preserving). That is, spaces are the "free" cocomplete $\infty$-category on a single object, in the same way that sets are the free ordinary cocomplete category on a point. | |
| Jul 17, 2012 at 15:23 | answer | added | Tim Porter | timeline score: 4 | |
| Jul 17, 2012 at 14:35 | comment | added | Mirco A. Mannucci | Thanks Qiaochu! Yes, Peter's answer seems to be (very) relevant, as it singles out the simplicial homotopy nicely. Perhaps that can lead to a full answer to my 'dream", need some time to think about it... | |
| Jul 17, 2012 at 14:20 | comment | added | Qiaochu Yuan | In particular, Peter Arndt's answer (I hadn't noticed this) describes a universal property. | |
| Jul 17, 2012 at 14:17 | comment | added | Qiaochu Yuan | The discussion at mathoverflow.net/questions/58497/… seems relevant. | |
| Jul 17, 2012 at 14:02 | history | asked | Mirco A. Mannucci | CC BY-SA 3.0 |