Timeline for Does every morphism BG-->BH come from a homomorphism G-->H?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 28, 2009 at 4:33 | vote | accept | Anton Geraschenko | ||
| Oct 22, 2009 at 8:03 | comment | added | Bhargav | I think yes, though the triviality of what I'm thinking makes me think I'm missing something. Map(BG,Y) is equivalent to the groupoid of pairs (y in Y(k),f:G-> Aut(y) alg. homomorphism) with obvious groupoid structure. This obvious groupoid structure comes just from Y. Now assume Y(k) is connected. If we pick a point of Y(k) with k-automorphism group scheme H, then the resulting description is exactly what you suggest. | |
| Oct 22, 2009 at 7:20 | comment | added | Reid Barton | Is it true under the conditions of your last sentence that the groupoid of maps from BG to BH is equivalent to the category of functors from BG to BH as ordinary groupoids, i.e., the groupoid whose objects are conjugacy classes of maps and where the group of automorphisms of a map is its centralizer? | |
| Oct 22, 2009 at 5:11 | history | answered | Bhargav | CC BY-SA 2.5 |