  The paper explores some algebraic constructions arising in the theory of
Lefschetz fibrations. Specifically, it covers in a fair amount of detail the
algebraic issues outlined in ``Symplectic homology as Hochschild homology''
(math.SG/0609037). We also explain how the theory works when applied to a
simple example, namely the Landau-Ginzburg mirror of P^2.
  Version 2: revised, many technical assumptions dropped, statement of one of
the main results improved by using dg quotients. I changed the title
accordingly.

K-Theory and Homology;Rings and Algebras;Symplectic Geometry