  We consider local operators of CFT inserted at the boundary of the worldsheet
and an infinite set of maps that act on a space of the local operators. These
maps have natural CFT interpretation and form A-infinity algebra. In terms of
these operators we define the homotopical Maurer-Cartan equation, find its
symmetries and explore its properties. Further we recover the Yang-Mills
equation from the homotopical Maurer-Cartan equation, identify the first
alpha'-correction to it and propose method for calculation all corrections.
