The Fukaya category of a fibration with singularities W: M --> C, or Fukaya-Seidel category, enlarges the Fukaya category of M by including certain non-compact Lagrangians and asymmetric perturbations at infinity involving W; objects include Lefschetz thimbles if W is a Lefschetz fibration. I will recall this category and then explain a criterion, in the spirit of work of Abouzaid and Abouzaid-Fukaya-Oh-Ohta-Ono, for when a finite collection of Lagrangians split-generates such a fibration. The new ingredients needed include a Floer homology group associated to (M,W) and the Serre functor. This is work in progress with Mohammed Abouzaid.