  We discuss a relationship between Khovanov- and Heegaard Floer-type homology
theories for braids. Explicitly, we define a filtration on the bordered
Heegaard-Floer homology bimodule associated to the double-branched cover of a
braid and show that its associated graded bimodule is equivalent to a similar
bimodule defined by Khovanov and Seidel.
