  We study homological mirror symmetry for toric varieties, exploring the
relationship between various Fukaya-Seidel categories which have been employed
for constructing the mirror to a toric variety. In particular, we realize
tropical Lagrangian sections as objects of a partially wrapped category and
construct a Lagrangian correspondence mirror to the inclusion of a toric
divisor. As a corollary, we prove that tropical sections generate the
Fukaya-Seidel category, completing a Floer-theoretic proof of homological
mirror symmetry for projective toric varieties. In the course of the proof, we
develop techniques for constructing Lagrangian cobordisms and Lagrangian
correspondences in Liouville domains, which may be of independent interest.
