  We study boundary conditions and defects in a three-dimensional topological
sigma-model with a complex symplectic target space X (the Rozansky-Witten
model). We show that boundary conditions correspond to complex Lagrangian
submanifolds in X equipped with complex fibrations. The set of boundary
conditions has the structure of a 2-category; morphisms in this 2-category are
interpreted physically as one-dimensional defect lines separating parts of the
boundary with different boundary conditions. This 2-category is a
categorification of the Z/2-graded derived category of X; it is also related to
categories of matrix factorizations and a categorification of deformation
quantization (quantization of symmetric monoidal categories). In the appendix
we describe a deformation of the B-model and the associated category of branes
by forms of arbitrary even degree.
