We want to find a full subcategory of a wrapped Fukaya category such that every object in the wrapped Fukaya category can be construced by the interated mapping cone of generating objects in the subcategory. Abouzaid states the criterion: If the identiy lies in the image of the open-closed map from the Hochschild homology of the subcategory to the symplectic cohomology of a Louville symplectic manifold. We will outline the ideal of the proof.

 

Ref:

M. Abouzaid “A geometric criterion for generating the Fukaya category”