  To a symplectic Lefschetz pencil on a monotone symplectic manifold, we
associate an algebraic structure, which is a pencil of categories in the sense
of noncommutative geometry. One fibre of this "noncommutative pencil" is
related to the Fukaya category of the open (meaning, with the base locus
removed, and hence exact symplectic) fibre of the original Lefschetz pencil;
the other fibres are newly constructed kinds of Fukaya categories.
