  We discuss D-branes of the topological A-model (A-branes), which are believed
to be closely related to the Fukaya category. We give string theory arguments
which show that A-branes are not necessarily Lagrangian submanifolds in the
Calabi-Yau: more general coisotropic branes are also allowed, if the line
bundle on the brane is not flat. We show that a coisotropic A-brane has a
natural structure of a foliated manifold with a transverse holomorphic
structure. We argue that the Fukaya category must be enlarged with such objects
for the Homological Mirror Symmetry conjecture to be true.
