For given a Lagrangian in a symplectic manifold, one can consider deformation of A-infinity algebra structures on its Floer complex by degree 1 elements satisfying the Maurer-Cartan equation. The space of such degree 1 elements can be thought of as giving a local chart of the mirror. In this talk, I will explain how to glue local charts from different Lagrangians using isomorphisms between Lagrangians in the Fukaya category.   As an application, we will discuss the mirror construction for Gr(2,4) that recovers its Lie-theoretical mirror.