  We introduce a contravariant functor, called Floer functor, from the category
of Lagrangian conductors of a symplectic manifold to the homotopy category of
bounded chain complexes of open strings in this manifold. The latter two
categories are defined for all symplectic manifolds, whereas Floer functor is
defined for semipositive manifolds which are either closed or convex at
infinity. We then prove that when the first Chern class of the symplectic
manifold vanishes, Lagrangian spheres define Lagrangian conductors so that in
particular their integral Floer cohomology is well defined. This requires the
introduction of singular almost-complex structures given by symplectic field
theory.
