I show that the category of D-branes of type A on a Calabi-Yau manifold may
contain
objects other than Lagrangian submanifolds with flat vector bundles or
their bound states.
Examples of non-Lagrangian A-branes are provided by coisotropic
submanifolds carrying
line bundles of a very special kind. I discuss how to generalize the Floer
homology to coisotropic A-branes.
I also discuss the significance of non-Lagrangian A-branes for the
Homological Mirror Conjecture.
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