Timeline for What information is lost in $X \to \mathrm{Sh}(X)$?
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| Feb 21, 2018 at 22:11 | answer | added | Qfwfq | timeline score: 1 | |
| Feb 21, 2018 at 18:28 | answer | added | Oscar Cunningham | timeline score: 2 | |
| Jun 3, 2014 at 12:54 | comment | added | Benjamin Steinberg | @MartinBrandenburg, I wrote my comment as an answer as requested. | |
| Jun 3, 2014 at 12:51 | answer | added | Benjamin Steinberg | timeline score: 16 | |
| Jun 3, 2014 at 11:56 | comment | added | Martin Brandenburg | @Benjamin: What about turning your comments into an answer? | |
| S May 31, 2014 at 2:52 | history | suggested | user62675 | CC BY-SA 3.0 |
changed some LaTex
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| May 31, 2014 at 2:17 | review | Suggested edits | |||
| S May 31, 2014 at 2:52 | |||||
| May 30, 2014 at 23:45 | comment | added | Zhen Lin | I notice that the OP also asks about sites. For general sites, much information is lost: two different sites can become equivalent after passing to sheaves. | |
| May 30, 2014 at 22:24 | comment | added | Benjamin Steinberg | To give a more precise answer, from Sh(X) one can recover the sober reflection of $X$ (the adjoint of the forgetful functor from sober spaces to spaces). | |
| May 30, 2014 at 22:17 | comment | added | Steven Landsburg | @BenjaminSteinberg: I realize I'm being pedantic, but your statement could have been read as saying (incorrectly) that if the categories of sheaves on $X$ and $Y$ are equivalent, and if $X$ is sober, then $X$ is homeomorphic to $Y$. To make the statement correct, one needs the additional hypothesis that $Y$ (not just $X$) is sober. | |
| May 30, 2014 at 21:25 | comment | added | Benjamin Steinberg | @Steven, what else could I have meant? | |
| May 30, 2014 at 21:24 | comment | added | Qiaochu Yuan | I think the general statement is that you can recover precisely the frame of open subsets on $X$, and that sober spaces are those spaces which can be recovered from their frame of open subsets. | |
| May 30, 2014 at 21:16 | comment | added | Steven Landsburg | You have to be a little careful saying "For a sober space nothing is lost". The fact that $X$ is sober does not mean that I can reconstruct $X$ from $Sh(X)$. It does mean that I can reconstruct $X$ from $Sh(X)$ together with the knowledge that $X$ is sober. | |
| May 30, 2014 at 21:11 | comment | added | Benjamin Steinberg | For a sober space nothing is lost | |
| S May 30, 2014 at 20:57 | review | First posts | |||
| May 30, 2014 at 20:59 | |||||
| S May 30, 2014 at 20:57 | review | Close votes | |||
| May 31, 2014 at 4:39 | |||||
| S May 30, 2014 at 20:55 | history | edited | Mark Wildon | CC BY-SA 3.0 |
typo edited
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| S May 30, 2014 at 20:55 | history | suggested | user21574 | CC BY-SA 3.0 |
typo edited
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| May 30, 2014 at 20:53 | review | Suggested edits | |||
| S May 30, 2014 at 20:55 | |||||
| May 30, 2014 at 20:37 | history | asked | Adrian | CC BY-SA 3.0 |