The main goal of this paper is to discuss a symplectic interpretation of
Lipshitz, Ozsvath and Thurston's bordered Heegaard-Floer homology in terms of
Fukaya categories of symmetric products and Lagrangian correspondences. More
specifically, we give a description of the algebra A(F) which appears in the
work of Lipshitz, Ozsvath and Thurston in terms of (partially wrapped) Floer
homology for product Lagrangians in the symmetric product, and outline how
bordered Heegaard-Floer homology itself can conjecturally be understood in this
language.