Timeline for Has any attempt been made to classify finite groupoids?
Current License: CC BY-SA 3.0
15 events
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| Oct 26, 2017 at 10:30 | history | edited | Martin Sleziak |
Removed deprecated (discrete-mathematics) tag - see the tag info: https://mathoverflow.net/tags/discrete-mathematics/info (if there are some other suitable tags, choose some of them instead)
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| Mar 27, 2015 at 1:46 | answer | added | Qiaochu Yuan | timeline score: 11 | |
| Feb 27, 2013 at 18:19 | comment | added | Todd Trimble | Indeed, it is more correct to say that groups are equivalent to pointed connected groupoids. See the appendix in Baez and Shulman's article: arxiv.org/abs/math/0608420, p. 50 and following. | |
| Feb 27, 2013 at 15:10 | answer | added | Ronnie Brown | timeline score: 15 | |
| Feb 26, 2013 at 22:29 | comment | added | Ronnie Brown | @Fernando:Your remark about being "the same" does not apply to many structured groupoids, e.g. groupoids with a group structure, or topology. Interestingly, there is at present no "noncommutative geometry" applied to algebraically structured groupoids. But just looking at the fact that higher groupoids are much more complicated than groups, led me to ask how they can be used in higher homotopy theory, and elsewhere, even without knowing that $n$-fold groupoids classify weak homotopy $n$-types, to which Grothendieck exclaimed: "That is absolutely beautiful!" | |
| Nov 29, 2012 at 1:33 | comment | added | David Roberts♦ | Silly question: what is $\pi_0(M_{13})$ (the set of isomorphism classes)? Note that the 2008 article The transitivity of Conway's $M_{13}$ linked to on the Wikipedia page is not about the concept of groupoid transitivity. | |
| Nov 28, 2012 at 10:57 | answer | added | S. Carnahan♦ | timeline score: 6 | |
| Nov 27, 2012 at 16:05 | answer | added | Ben Fairbairn | timeline score: 31 | |
| Oct 6, 2012 at 19:00 | comment | added | Fernando Muro | @Ronnie: a connected groupoid is the same as a group if we look through the glasses of equivalences of categories, which I think of as the right notion of 'bein the same' in this context. | |
| Oct 6, 2012 at 13:52 | comment | added | Ronnie Brown | @Fernado: I think you mean: any groupoid is a disjoint union of connected groupoids. A;ex Heller once remarked to me that the classification of vector spaces is easy, but the classification of vector spaces with one endomorphism is both interesting and non trivial; with two endomorphisms is hard; and with three is unsolved. So I think in this example we are given more than just a groupoid-see my comment below. | |
| Oct 6, 2012 at 9:56 | comment | added | Fernando Muro | Any groupoid is a disjoint union of groups, so classifying finitie groups or finite groupoids are the same problem. | |
| Oct 6, 2012 at 5:51 | comment | added | Todd Trimble | I guess all I'm saying in my answer is that there has been an "attempt to classify finite groupoids" to the same exact extent that there has been an attempt to classify finite groups. I honestly don't know what exactly has been achieved in this regard, but last I heard, we are extremely far away from that. | |
| Oct 6, 2012 at 5:27 | history | edited | temp | CC BY-SA 3.0 |
added 4 characters in body
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| Oct 6, 2012 at 5:12 | answer | added | Todd Trimble | timeline score: 26 | |
| Oct 6, 2012 at 3:42 | history | asked | temp | CC BY-SA 3.0 |