  We develop a local-to-global formalism for constructing Calabi-Yau structures
for global sections of constructible sheaves or cosheaves of categories. The
required data - an isomorphism of the sheafified Hochschild homology with the
topological dualizing sheaf - specializes to the classical notion of
orientation when applied to the category of local systems on a manifold. We
apply this construction to the cosheaves on arboreal skeleta arising in the
microlocal approach to the A-model.
