Timeline for Are there examples where one proves something about the functor represented by an object using the functor it corepresents?
Current License: CC BY-SA 2.5
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Apr 25, 2010 at 0:58 | comment | added | JBorger | Yeah, I think that's an excellent general remark. For quotients in sheaf theory, maps out and maps in are not so far apart. I wonder if this is in some sense part of the reason why sheaf theory is such a useful formalism. | |
| Apr 25, 2010 at 0:48 | comment | added | BCnrd | Jim, how about this: we often need to study the "points" of a coset space $G/H$ (valued in various rings, like interesting fields), and sometimes do so by working etale-locally or fppf-locally and lifting to points of $G$. The lifting step involves the viewpoint of the quotient sheafification by which $G/H$ is characterized by maps out of it (whereas the "points" considered above involve maps into $G/H$). And likewise in many other quotient situations (for algebraic spaces, sheaves of various sorts, etc.) | |
| Apr 24, 2010 at 22:06 | answer | added | JBorger | timeline score: 0 | |
| Apr 24, 2010 at 16:40 | answer | added | S. Carnahan♦ | timeline score: 4 | |
| Apr 19, 2010 at 22:59 | answer | added | Martin Brandenburg | timeline score: 0 | |
| Mar 14, 2010 at 11:29 | comment | added | Regenbogen | If you have such a theorem, then by Yoneda, you can anyway express it in terms of properties of $Hom(_,X)$. | |
| Mar 14, 2010 at 7:19 | history | asked | JBorger | CC BY-SA 2.5 |