Timeline for A few general questions about pre-sheaves and sheaves
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jun 14, 2018 at 19:30 | comment | added | Fan Zheng | @Malkoun: A HUGE Sorry. What happened is that I opened too many mathoverflow tags and copied the wrong address. LInk has been fixed. | |
| Jun 14, 2018 at 19:26 | history | edited | Fan Zheng | CC BY-SA 4.0 |
deleted 48 characters in body
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| Jun 14, 2018 at 11:09 | comment | added | Malkoun | I think this page needs some cleaning up. | |
| Jun 14, 2018 at 10:34 | comment | added | Maxime Ramzi | @WillSawin ah ok seeing $L:\mathbf{Psh}(X) \to \mathbf{Psh}(X)$. Since this is a tiny bit subtle it's good to make it clear haha | |
| Jun 14, 2018 at 10:27 | comment | added | Will Sawin | @Max I was referring to the sheafificatiin functor from presheaves to presheaves . It's all the same. | |
| Jun 14, 2018 at 9:13 | comment | added | Maxime Ramzi | @WillSawin probably the actual reason is that in my "proof" the second $\bigoplus$ is the direct sum in $\mathbf{Sh}(X)$ (I realized my blunder too late) and this does not coincide with the direct sum in $\mathbf{Psh}(X)$ (the inclusion functor does not commute with direct sums, while the sheafification functor does) | |
| Jun 14, 2018 at 7:37 | comment | added | Will Sawin | @BrianT Sheafification doesn't commute with direct sum as the definition of sheafification involves products, possibly infinite, and infinite products don't commute with infinite sums. | |
| Jun 14, 2018 at 7:04 | comment | added | Malkoun | I did some search, and indeed, some counterexamples can be found for example here: math.stackexchange.com/questions/193816/… | |
| Jun 14, 2018 at 6:29 | comment | added | BrianT | Hi Fan Zheng, so can you tell me where the above argument of Max fails : let $F^l$ be sheaves, and $F$ be the functor sheafification. Then $$F(\underset{l}{\bigoplus} F^l) = \underset{l}{\bigoplus} F(F^l) = \underset{l}{\bigoplus} F^l$$ | |
| Jun 14, 2018 at 4:33 | comment | added | Malkoun | Hi. I followed the link, but could not find the counterexample. Do you mean in Ravi Vakil's notes? | |
| Jun 14, 2018 at 0:13 | history | answered | Fan Zheng | CC BY-SA 4.0 |