Timeline for What is the 2-category whose 0-objects are Lie algebroids?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 1, 2010 at 16:08 | comment | added | Chris Schommer-Pries | I posted an answer that builds on Konrad's here. Basically you want to replace "isomorphism" with a certain class of Lie algebroid homomorphisms. These homomorphisms come from Morita equivalences of Lie groupoids, and the bicategory you get is a variation on the bicategory of spans. It formally inverts these special homomorphisms. | |
| Jul 31, 2010 at 18:11 | history | edited | Konrad Waldorf | CC BY-SA 2.5 |
added 181 characters in body
|
| Jul 31, 2010 at 18:08 | comment | added | Konrad Waldorf | Ah, interesting! Right, I must not require that one of the Lie algebroid morphisms is an iso. So the actual question is: if F is a smooth essentially surjective full and faithful functor between Lie groupoids, which properties characterize the induced map on Lie algebroids? | |
| Jul 31, 2010 at 13:21 | comment | added | Theo Johnson-Freyd | This certainly defines a 2-category, but as I mentioned in the comments, it will not lead to non-isomorphic equivalent Lie algebroids, and in particular will not accept a 2-functor from the bibundle category of groupoids that on objects takes a groupoid to its tangent-along-the-identity-section algebroid. So you have defined a 2-category whose 0-objects are Lie algebroids, but not the 2-category whose 0-objects are Lie algebroids :) | |
| Jul 31, 2010 at 4:39 | history | edited | Konrad Waldorf | CC BY-SA 2.5 |
added 53 characters in body
|
| Jul 31, 2010 at 4:16 | history | answered | Konrad Waldorf | CC BY-SA 2.5 |