Timeline for Internal hom of sheaves
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 14, 2010 at 16:19 | answer | added | Urs Schreiber | timeline score: 1 | |
| Mar 18, 2010 at 11:41 | comment | added | roger123 | The "second definition" is from "Sheaves in geometry and logic" "Mac Lane, Moerdijk" I. Proposition 1. and page 136. I don't remember where the first definition is from. | |
| Mar 18, 2010 at 1:51 | comment | added | Steven Gubkin | You really shouldn't be defining sheaf hom in any of these ways - you should be defining it by it's universal property. That is the right way to think about it - you have just presented some constructions. How do you verify if your constructions are valid? Check the property. For a very nice treatment of all of this see MacLane's "Sheaves in Geometry and Logic". | |
| Mar 18, 2010 at 0:50 | comment | added | Agustí Roig | Sorry roger123, but where do you find "in the literature" the two definitions? Thanks in advance. | |
| Mar 18, 2010 at 0:11 | answer | added | David Carchedi | timeline score: 5 | |
| Mar 17, 2010 at 11:48 | comment | added | roger123 | You are right, Omar. But this is strange: Look at Shafarevic, Basic Algebraic Geometry 2, VI.3.2. Example 2 (page 88). "the dual sheaf ... is the sheafication of the presheaf $G(U)=Hom(F(U),O_X(U))$". | |
| Mar 16, 2010 at 15:54 | comment | added | Omar Antolín-Camarena | The third definition you suggest (in the edit) doesn't work: that formula does not define a presheaf; there is no way to define the restriction maps. | |
| Mar 16, 2010 at 13:10 | comment | added | roger123 | I made an edit. Perhaps it is better now | |
| Mar 16, 2010 at 13:07 | history | edited | roger123 | CC BY-SA 2.5 |
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| Mar 16, 2010 at 11:59 | answer | added | Peter Arndt | timeline score: 3 | |
| Mar 16, 2010 at 11:48 | comment | added | Andrea Ferretti | I don't understand the notation for the second definition. | |
| Mar 16, 2010 at 11:28 | history | edited | roger123 | CC BY-SA 2.5 |
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| Mar 16, 2010 at 10:54 | history | asked | roger123 | CC BY-SA 2.5 |