Timeline for Descent of Morphisms of Sheaves
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 3, 2015 at 0:58 | comment | added | Ben | (Because $f$ is not just open but a local homeomorphism, the equality holds locally, which is all that is needed.) | |
| Sep 3, 2015 at 0:02 | comment | added | Ben | That $f$ is open allows the limit to be dropped, but not the sheafification; in general $\Gamma(Y,f^{-1}A) \not= A(f(Y))$, for example pull back the Mobius bundle on $S^1$ to $\mathbb{R}$. | |
| May 10, 2012 at 20:07 | vote | accept | cheyne | ||
| May 10, 2012 at 16:41 | comment | added | Moshe | I'm not sure about the etiquette, I'm also not a very active participant... As for the second part, this is the same as saying that $(A\times B)\times C$ is not equal to $A\times(B\times C)$. This is formally true, but mostly irrelevant, since there is a canonical isomorphism. The same happens with pullbacks of sheaves, but in the abstract framework you have to be given this isomorphism, and I guess the book is trying to motivate this. In my personal opinion, this point is often stressed way beyond its importance... | |
| May 10, 2012 at 16:28 | comment | added | cheyne | OK thanks. Now, I am thinking about my second question. Is it a bad idea to call yours an "answer" before the second part is answered? Then people won't offer answers to the second question? I'm new to this forum. And agree with you that the idea is to motivate more general concepts. | |
| May 10, 2012 at 13:46 | history | answered | Moshe | CC BY-SA 3.0 |