  Motivated by the path integral analysis of boundary conditions in a
3-dimensional topological sigma-model, we suggest a definition of the
2-category associated with a holomorphic symplectic manifold X and study its
properties. The simplest objects of this 2-category are holomorphic lagrangian
submanifolds of X. We pay special attention to the case when X is the total
space of the cotangent bundle of a complex manifold U or a deformation thereof.
In the latter case the endomorphism category of the zero section is a monoidal
category which is an A-infinity deformation of the 2-periodic derived category
of U.
