Timeline for Why isn't $BG$ a group, for $G$ not abelian?
Current License: CC BY-SA 3.0
7 events
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| Jun 30, 2013 at 5:09 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Jun 29, 2013 at 18:54 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Jun 29, 2013 at 18:52 | comment | added | Qiaochu Yuan | @Joe: yes, but in with the latter argument we only get a group structure on the homotopy type of $BG$, whereas with an appropriate construction of $B$ we should get a group structure on an actual topological space. | |
| Jun 29, 2013 at 18:43 | comment | added | ziggurism | So we have two ways to see that $BG$ is a group when $G$ is abelian, 1. $B$ is monoidal functor, and 2. $BG$ represents $H^1(-;G)$ which has an obvious group structure which descends to $BG$ by Yoneda. I just learned that second one from Andrew Stacey here: mathoverflow.net/questions/12469/group-structure-on-cpinfinty | |
| Jun 29, 2013 at 18:38 | vote | accept | ziggurism | ||
| Jun 29, 2013 at 18:38 | comment | added | ziggurism | Of course! The group objects are abelian groups. Thank you | |
| Jun 29, 2013 at 18:36 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |