Timeline for What's the easiest example of a morphism of topoi that is not from that of a site?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 1, 2011 at 4:07 | comment | added | Mike Shulman | Qfwfq: Yes, it is. In fact, for any geometric morphism $f:X\to Y$, we can pick any site $S_Y$ generating $Y$, and then there exists a site $S_X$ generating $X$ for which $f$ is induced by a map of sites $S_Y\to S_X$. | |
| Oct 31, 2011 at 21:30 | history | edited | JBorger | CC BY-SA 3.0 |
added 3 characters in body
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| Oct 31, 2011 at 18:16 | comment | added | Qfwfq | If the above is true, it reminds me of the fact that you can present (nice) topological spaces $X,Y$ as simplicial complexes $S_X,S_Y$ but if the latter are too "coarse" there may be maps $f:X\to Y$ that are not realized (up to homotopy) by simplicial maps $S_X\to S_Y$; nevertheless you can always present $X$ and $Y$ by "finer" simplicial complexes such that a simplicial approximation to $f$ does exist. | |
| Oct 31, 2011 at 18:11 | comment | added | Qfwfq | Is it true that for every (Grothendieck) topos morphism $f:X\to Y$ you can choose sites $S_X$ and $S_Y$, with $X=Sh(S_X)$ and $Y=Sh(S_Y)$, such that $f$ comes from a morphism of sites $\varphi: S_X\to S_Y$ ? | |
| Oct 31, 2011 at 11:48 | comment | added | Yosemite Sam | +1 - I guess one could also take $\mathbb{R}^n$ and the sites of open subsets and open balls. | |
| Oct 31, 2011 at 8:01 | history | answered | JBorger | CC BY-SA 3.0 |