Timeline for Is there something interesting in the uniqueness condition for a sheaf?
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| Nov 16, 2012 at 3:54 | comment | added | anon | Well, all "natural" presheafs are presheafs of functions, for which uniqueness is automatic. However, the presheaf quotient of a sheaf by a subpresheaf need not satisfy uniqueness. For example, consider at the presheaf quotient of the sheaf of locally constant functions on a space by the subpresheaf of constant functions. | |
| Nov 16, 2012 at 3:52 | comment | added | Tom Leinster | The answer, of course, depends on which presheaves you count as natural or non-pathological. If you're only willing to consider presheaves F on X of the type "F(U) = {functions on X satisfying some condition}" then you're always going to have uniqueness. | |
| Nov 16, 2012 at 0:43 | history | asked | Luis Felipe | CC BY-SA 3.0 |