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We study homological mirror symmetry for toric varieties, exploring therelationship between various Fukaya-Seidel categories which have been employedfor constructing the mirror to a toric variety. In particular, we realizetropical Lagrangian sections as objects of a partially wrapped category andconstruct a Lagrangian correspondence mirror to the inclusion of a toricdivisor. As a corollary, we prove that tropical sections generate theFukaya-Seidel category, completing a Floer-theoretic proof of homologicalmirror symmetry for projective toric varieties. In the course of the proof, wedevelop techniques for constructing Lagrangian cobordisms and Lagrangiancorrespondences in Liouville domains, which may be of independent interest.

Aspects of functoriality in homological mirror symmetry for toric varieties