Abstract: We explain a construction of a homological mirror symmetry functor using a formal deformation theory of a Lagrangian in a symplectic manifold. As an example, we will discuss examples of elliptic curve quotients. It can be generalized to the non-commutative setting, where the formalism provides a mirror that is a non-commutative algebra with a central element, together with a functor from Fukaya category to the matrix factorization category of the central element. This is a joint work with Hansol Hong and Siu-Cheong Lau.