Timeline for Presheaves are locally sheaves?
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 14, 2011 at 0:14 | comment | added | Georges Elencwajg | Dear George, the world would be a much better place if more people were willing to say they had been wrong and apologized. You have all my admiration for your last comment. | |
| Jan 13, 2011 at 1:29 | answer | added | roy smith | timeline score: 4 | |
| Jan 12, 2011 at 13:24 | comment | added | Harry Gindi | -1: Daniel, did you ever think to look up the page local isomorphism on the nLab: ncatlab.org/nlab/show/local+isomorphism ? Also, the definition in terms of Grothendieck topologies is a necessary complication of the theory WRT local isomorphisms (or else we're left with only the trivial case). See my comment on Clark Barwick's answer. | |
| Jan 12, 2011 at 0:51 | comment | added | George Lowther | Evidently, my previous comment was wrong. Sorry. | |
| Jan 12, 2011 at 0:14 | vote | accept | Daniel Barter | ||
| Jan 11, 2011 at 18:16 | comment | added | Urs Schreiber | The statement in the nLab entry about local isomorphism is correct, with the definition of local isomorphism as given at the page linked to: the canonical morphism from a presheaf to its sheaffification is a morphism that becomes an isomorphism under sheafification. Such morphisms are traditionally called local isomorphisms. And yes, this is a special case of the general theory of left exact reflective localizations. | |
| Jan 11, 2011 at 14:13 | comment | added | Buschi Sergio | Give a presheaf $F$, any the section $s\in Sh(F)(U)$ of the associated sheaf are locally sections of the presheaf i.e exist a covering $U=\cup_i U_i$ such that any restriction $s_{|U_i}$ come from (by the reflection map $r_{U_i}: F(U_i)\to Sh(F)(U_i)$) a section of the presheaf. | |
| Jan 11, 2011 at 8:48 | answer | added | Georges Elencwajg | timeline score: 14 | |
| Jan 11, 2011 at 3:38 | answer | added | Clark Barwick | timeline score: 18 | |
| Jan 11, 2011 at 3:37 | comment | added | George Lowther | But, having said that, I don't think this question is really suitable here. Maybe math.stackexchange would be a better place? | |
| Jan 11, 2011 at 3:35 | comment | added | George Lowther | Given that they defined a sheaf in terms of Grothendieck topologies, its not surprising that their other definitions involve them. If you're not dealing with such things I guess you could drop the Grothendieck bit. And the statement that presheaves are locally isomorphic to sheaves is almost tautological, given their definition of local isomorphism = isomorphism after passing to sheaves. | |
| Jan 11, 2011 at 3:17 | history | asked | Daniel Barter | CC BY-SA 2.5 |