Timeline for How should I think about delooping?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| May 20, 2020 at 15:26 | comment | added | Mike Shulman | @Student An ordinary 1-group $G$ can be delooped infinitely many times as soon as it is abelian. For an $n$-group or $\infty$-group, there is a hierarchy of "more and more commutativity": an $E_n$-group can be delooped $n$ times. | |
| May 19, 2020 at 18:25 | comment | added | Student | For a group $G$ to be delooped 3 times or above (and pertains the higher groupoid structures), what extra structure should it have? | |
| Oct 10, 2010 at 4:18 | comment | added | Mike Shulman | It does. In fact, only a non-simply-connected space can be modeled by a non-discrete groupoid, since the automorphism groups of the groupoid specify the $\pi_1$s of the space. | |
| Oct 10, 2010 at 2:32 | comment | added | Aaron Mazel-Gee | I do like this. In my imaginary autobiography, this chapter of my life will be entitled "How I learned to stop worrying and love category theory". Why doesn't the identification with groupoids extend to an equivalence involving non-simply-connected spaces, though? This seems like it's probably answered in your second paragraph, but I can't figure it out. | |
| Oct 8, 2010 at 23:09 | history | answered | Mike Shulman | CC BY-SA 2.5 |