Timeline for About the canonical morphism from $f^{*}f_{*}f^{*}F$ to $f^{*}F$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 13, 2015 at 11:16 | vote | accept | Bernie | ||
| Oct 12, 2015 at 19:29 | comment | added | eric | Take a step back. All these sorts of adjoint arguments just spit out "the only map you can think of", and so of course (*) will just be the pullback of the canonical morphism and will hence be an isomorphism (because the pullback of an iso is an iso). You should try to turn this into a proof but this should surely be how you are thinking. | |
| Oct 12, 2015 at 18:03 | answer | added | Zhen Lin | timeline score: 5 | |
| Oct 12, 2015 at 18:03 | comment | added | Matthias Wendt | The definition of adjoint functor implies that the composition $f^\ast F\to f^\ast f_\ast f^\ast F\to f^\ast F$ is the identity. Since the first map is an isomorphism in your situation, then so is the second, which is the canonical map ($\ast$). | |
| Oct 12, 2015 at 17:40 | history | asked | Bernie | CC BY-SA 3.0 |