Timeline for Why the third stage of Cech nerve a Lie 2-groupoid?
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Aug 22, 2020 at 15:47 | vote | accept | Adittya Chaudhuri | ||
| Aug 22, 2020 at 15:47 | |||||
| Mar 12, 2020 at 2:19 | answer | added | Bumblebee | timeline score: 0 | |
| Mar 4, 2020 at 11:19 | comment | added | Adittya Chaudhuri | @DmitriPavlov Sir, I wrote an answer(with some doubts stated) in response to your comment above. Please can you check once in your free time and let me know whether it makes sense or not? ... Thanks in advance. | |
| Mar 4, 2020 at 11:17 | answer | added | Adittya Chaudhuri | timeline score: 0 | |
| Mar 4, 2020 at 6:49 | comment | added | Adittya Chaudhuri | @DmitriPavlov Thanks for the comment. I got where I was making the mistake. I am trying to understand the 2 categorical simplicial model(as you have mentioned in the comment. ) | |
| Mar 4, 2020 at 3:14 | answer | added | Praphulla Koushik | timeline score: 1 | |
| Mar 3, 2020 at 21:06 | comment | added | Dmitri Pavlov | @AdittyaChaudhuri: No, it doesn't work this way. The 2-categorical model used here is simplicial, so a 2-morphism is an arrow fh→g, where f, g, h are 1-morphisms given by the three simplicial faces of this 2-simplex. In the case under consideration, these three faces are given by mapping U_i∩U_j∩U_k into U_j∩U_k, U_i∩U_k, and U_i∩U_j respectively. | |
| Mar 3, 2020 at 17:36 | comment | added | Adittya Chaudhuri | @PraphullaKoushik Please see the comment above. | |
| Mar 3, 2020 at 17:33 | comment | added | Adittya Chaudhuri | @DmitriPavlov Thanks for the comment and the link. I also guessed that the space of all 2-morphisms is $(\sqcup{U_{i}\cap U_{j}\cap U_{k}})$. But I am not able to figure out that for a general 2 morphism $(x,i,j,k)$ what will be its source(1-morphism) and target(1-morphism)? I hope the space of 1-morphisms will be $(\sqcup{U_{i}\cap U_{j}})$ where the source and target of a general 1-morphism $(x,i,j)$ are $(x,i)$ and $(x,j)$ respectively. | |
| Mar 3, 2020 at 17:15 | comment | added | Adittya Chaudhuri | @PraphullaKoushik Thanks for the link. From the link, it seems what I guessed about the definition of Lie 2-Groupoid is right. | |
| Mar 3, 2020 at 14:25 | comment | added | Dmitri Pavlov | The space of all 2-morphisms in the Lie 2-groupoid under consideration is the disjoint union of U_i ∩ U_j ∩ U_k. The correspondence between various flavors of 2-categories and simplicial objects is explained in ncatlab.org/nlab/show/geometric+nerve+of+a+bicategory | |
| Mar 3, 2020 at 13:21 | comment | added | Praphulla Koushik | what is the 1 morphism in Cech groupoid? | |
| Mar 3, 2020 at 13:13 | comment | added | Praphulla Koushik | Check last 1/4 th of page 9 and first 1/4 th of page 10 in arxiv.org/abs/1706.07152 | |
| Mar 3, 2020 at 12:21 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Mar 3, 2020 at 12:18 | history | edited | Adittya Chaudhuri | CC BY-SA 4.0 |
deleted 3 characters in body
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| Mar 3, 2020 at 12:13 | history | asked | Adittya Chaudhuri | CC BY-SA 4.0 |