Loopholes in Bell test experiments
Let X be a topological space, and denote the category of sheaves with values in . Then the map that associates to a sheaf its global sections is a covariant functor to .
If is the category of abelian groups, then this functor is left exact. This important remark leads to the notion of sheaf cohomology, via derived functors.
Examples
- Let be the locally constant sheaf. Then its global sections are given by , i.e. the direct sum indexed by connected components of X
- Let be the sheaf of holomorphic functions on the compact connected complex manifold X, then by the maximum principle, global sections are constant, ie.
- Let denote the twisting sheaves on the projective space , then for , and 0 for .