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The general definition of (last paragraph) is wrong. Check out this mathoverflow question.
Also I think that the example is far too long ... but this is just my opinion. -oo- ( talk) 10:30, 1 May 2010 (UTC)
In the "detailed example" why are there nine inclusions, and not five? 85.250.40.219 ( talk) 23:04, 14 January 2011 (UTC)
The text claims that F is a separated presheaf and satisfies the gluing axiom, but not a sheaf. I believe the usual definition of a "separated presheaf" is simply one which satisfies the identity axiom (if two sections of U agree on all the members of some open cover of U then they are the same), not a sheaf whose restriction maps are injective (this almost never happens!). Thus any separated presheaf which satisfies the gluing axiom is a sheaf... 2620:101:F000:700:223:6CFF:FE98:4D1 ( talk) 02:57, 6 August 2013 (UTC)
The comment(s) below were originally left at Talk:Constant sheaf/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
What is the normalization axiom? I don't find it anywhere. None of the books I've read about sheaves seem to mention it, and I can't find it online either. Carmen |
Last edited at 15:43, 11 December 2008 (UTC). Substituted at 01:55, 5 May 2016 (UTC)
By the stalks are "equal", does that mean they are literally equal? or up to an isomorphism? ? Or ? I think it should be the latter (it's similar to the change of base point functor) If so, the article needs to be clarified. -- Taku ( talk) 18:35, 9 July 2017 (UTC)
@ Jakob.scholbach thank you for your excellent detailed example on this page. It looks like it was migrated from Sheaf (mathematics) to this page based on looking at history.
I'm wondering if the use of ⊕ rather than ×/⊗ in the last part of the example is still correct. I read it as a coproduct, making me think of the Disjoint union (topology). Can the disjoint union hold enough information, though? Let's say we have the element (7,b) in ℤ⊕ℤ (where the b indicates that the number comes from the second ℤ set). Where would each of the projection morphisms map this? It seems like only one of the morphisms would be able to; the second wouldn't have enough information.
If you do think this should be changed then I can fix up the diagram tied to the text (I know that can be a headache), unless you want to. I'm obviously not certain that I'm understanding everything correctly, however. Davidvandebunte ( talk) 18:20, 6 December 2023 (UTC)
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
The general definition of (last paragraph) is wrong. Check out this mathoverflow question.
Also I think that the example is far too long ... but this is just my opinion. -oo- ( talk) 10:30, 1 May 2010 (UTC)
In the "detailed example" why are there nine inclusions, and not five? 85.250.40.219 ( talk) 23:04, 14 January 2011 (UTC)
The text claims that F is a separated presheaf and satisfies the gluing axiom, but not a sheaf. I believe the usual definition of a "separated presheaf" is simply one which satisfies the identity axiom (if two sections of U agree on all the members of some open cover of U then they are the same), not a sheaf whose restriction maps are injective (this almost never happens!). Thus any separated presheaf which satisfies the gluing axiom is a sheaf... 2620:101:F000:700:223:6CFF:FE98:4D1 ( talk) 02:57, 6 August 2013 (UTC)
The comment(s) below were originally left at Talk:Constant sheaf/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
What is the normalization axiom? I don't find it anywhere. None of the books I've read about sheaves seem to mention it, and I can't find it online either. Carmen |
Last edited at 15:43, 11 December 2008 (UTC). Substituted at 01:55, 5 May 2016 (UTC)
By the stalks are "equal", does that mean they are literally equal? or up to an isomorphism? ? Or ? I think it should be the latter (it's similar to the change of base point functor) If so, the article needs to be clarified. -- Taku ( talk) 18:35, 9 July 2017 (UTC)
@ Jakob.scholbach thank you for your excellent detailed example on this page. It looks like it was migrated from Sheaf (mathematics) to this page based on looking at history.
I'm wondering if the use of ⊕ rather than ×/⊗ in the last part of the example is still correct. I read it as a coproduct, making me think of the Disjoint union (topology). Can the disjoint union hold enough information, though? Let's say we have the element (7,b) in ℤ⊕ℤ (where the b indicates that the number comes from the second ℤ set). Where would each of the projection morphisms map this? It seems like only one of the morphisms would be able to; the second wouldn't have enough information.
If you do think this should be changed then I can fix up the diagram tied to the text (I know that can be a headache), unless you want to. I'm obviously not certain that I'm understanding everything correctly, however. Davidvandebunte ( talk) 18:20, 6 December 2023 (UTC)