  It is one of the most important problems in mirror symmetry to obtain
functorially Frobenius manifolds from smooth compact Calabi-Yau
$A_\infty$-categories. This paper gives an approach to this problem based on
the theory of primitive forms. Under an assumption on the formality of a
certain homotopy algebra, a formal primitive form for a smooth compact
Calabi-Yau dg algebra can be constructed, which enable us to have a formal
Frobenius manifold.
