  We prove the Strengthened Hanna Neumann Conjecture. We give a more direct
cohomological interpretation of the conjecture in terms of "typical" covering
maps, and use graph Galois theory to "symmetrize" the conjecture. The
conjecture is then related to certain kernel of a morphism of sheaves, and is
implied provided these kernels are co-acyclic in the covering cohomology
theory. This allows us to prove a slightly generalized Strengthened Hanna
Neumann Conjecture; this conjecture is false if generalized to all sheaves. The
kernels we use do not exist in the theory of graphs, so our use of sheaf theory
seems essential to this approach.
