• Construction from skeleton's core

Why do we have matrix factorization from mirror symmetry of pair-of-pants? The most elegant answer, I think, comes from Seidel's immersed Lagrangian trick. Consider the space of weakly bounding cochain, and the natural superpotential function on it. This is most natural, since we don't need to consider any critical points on the A-side at all. See Hansol's presentation

The deformation space is usually sitting inside the immersed Lagrangian's generator. When the immersed Lagrangian is simply a union of a bunch of smooth Lagrangians, one can ask, how does that endomorphism algebra work.