  We discuss aspects of topological B-type D-branes in the framework of the
derived category of coherent sheaves on a Calabi-Yau 3-fold X. We analyze the
link between massless D-branes and monodromies in the CFT moduli space. A
classification of all massless D-branes at any point in the moduli space is
conjectured, together with an associated monodromy. We test the conjectures in
two independent ways. First we establish a composition formula for certain
Fourier-Mukai functors, which is a consequence of the triangulated structure of
D(X). Secondly, using pi-stability we rederive the stable soliton spectrum of
the pure N=2 supersymmetric SU(2) Seiberg-Witten theory. In this approach, the
simplicity of the spectrum rests on Grothendieck's theorem concerning vector
bundles over P^1.
