Timeline for Groups lying horizontally in 2-groups
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 1, 2013 at 8:46 | vote | accept | Werner Thumann | ||
| Feb 1, 2013 at 8:45 | comment | added | Werner Thumann | Fernando, thank you for your help, I will think over all this. | |
| Feb 1, 2013 at 8:08 | comment | added | Fernando Muro | @Werner, free crossed modules are a special case of what you propose, hence the computation above works as a counterexample too. BTW, I think that, in general, free objects are not better behaved for this king of question, because they are universal examples, hence anything that fails in general fails also for free ones. | |
| Jan 31, 2013 at 22:55 | comment | added | Werner Thumann | @ Fernando, Chris, Evan: Thank you for your answers. Oh yes, this question is ill-posed. Consider e.g. the free 2-group generated by an object A and an iso from I to A. Then pi_1 is trivial and pi_2 also, so it is 2-equivalent to the trivial 2-group. But in the first case, the group I defined is ZxZ and in the second case trivial. Can someone confirm this. But maybe I can rescue a bit of the question by restricting to 2-groups freely gen. by some objects and some isos between tensor expressions of these objects. Can something be said in this case? | |
| Jan 31, 2013 at 21:03 | history | answered | Fernando Muro | CC BY-SA 3.0 |