Timeline for How to interpret topologically that the equalizer in Groupoids of ${\rm id}, {\rm id}: BG \rightrightarrows BG$ is $G/G$ (adjoint action)?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 16, 2011 at 6:39 | comment | added | Theo Johnson-Freyd |
Hrm, on my computer the equation Maps(S^1 -> BG) = G/G seems to print in the wrong place.
|
|
| Jan 16, 2011 at 6:38 | comment | added | Theo Johnson-Freyd |
So, just to emphasize this (and David Ben-Zvi also emphasizes this), I was wrong to read the first diagram as ${\rm B}G\times S^1$; rather, I should read it as $\operatorname{Maps}(S^1\to{\rm B}G)$. (Why?) Then the limit statement is precisely that $\operatorname{Maps}(S^1\to{\rm B}G)=G/G$ up to homotopy. (Why would this be the limit statement, and not, say, the colimit statement? Come to think of it: what's the colimit of that diagram?)
|
|
| Jan 16, 2011 at 6:32 | vote | accept | Theo Johnson-Freyd | ||
| Jan 15, 2011 at 19:09 | history | answered | Ben Webster♦ | CC BY-SA 2.5 |