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This is a sequel to our paper arXiv:2008.13462, where we proposed adefinition of the Morse homotopy of the moment polytope of toric manifolds.Using this as the substitute of the Fukaya category of the toric manifolds, weproved a version of homological mirror symmetry for the projective spaces andtheir products via Strominger-Yau-Zaslow construction of the mirror dualLandau-Ginzburg model. In this paper we go this way further and extend ourprevious result to the case of the Hirzebruch surface $\mathbb{F}_1$.

Homological mirror symmetry of $\mathbb{F}_1$ via Morse homotopy