Timeline for Mistake in Hartshorne's Exercise II.1.1?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 27, 2019 at 13:21 | comment | added | Laurent Moret-Bailly | Oh, I see. So Hartshorne has the wrong definition of a presheaf! In fact, it is not consistent with the other (correct) definition he gives immediately after (contravariant functor on the category of open subsets). | |
| Apr 27, 2019 at 8:01 | comment | added | Zariski93 | The empty set goes to the trivial abelian group given only by $0$. | |
| Apr 27, 2019 at 5:00 | review | Close votes | |||
| May 2, 2019 at 23:34 | |||||
| Apr 27, 2019 at 4:39 | comment | added | Laurent Moret-Bailly | In your definition of $\mathcal{A}$, what happens to the empty $U$? | |
| Apr 26, 2019 at 22:52 | comment | added | Zariski93 | You are right, thanks! | |
| Apr 26, 2019 at 22:48 | comment | added | Benjamin Steinberg | Continuous in the discrete topology means locally constant (I.e each point has a nbhd where the function is constant). Instead of covering U by connected components, choose an open cover by sets on which f is constant. You can even choose the open cover to be by disjoint open sets on which f is constant by using the full preimages of the elements of f(U). | |
| Apr 26, 2019 at 22:41 | history | asked | Zariski93 | CC BY-SA 4.0 |