We analyze the "geometric engineering" limit of a type II string on a suitable Calabi-Yau threefold to obtain an N = 2 pure SU(2) gauge theory. The derived category picture together with II-stability of B-branes beautifully reproduces the known spectrum of BPS solitons in this case in a very explicit way. Much of the analysis is particularly easy since it can be reduced to questions about the derived category of ℙ1. © SISSA/ISAS 2003.