Bohan Fang,
For the mirror curve of a toric Calabi-Yau 3-orbifold, one can assign a Fukaya-type category. This category is modeled on the category of constructible sheaves on the 1-dim Lagrangian core of the mirror curve. They form a cosheaf and also have some sheaf
TSIMF-Room A-211
Mirror curves and homological mirror symmetry for toric CY 3-orbifolds - Bohan Fang