Objects of the Fukaya category $F(V,\omega,J,\Omega)$ are triples
$(L,\rho,\widetilde{Arg}_{L})$, where $L$ is a compact oriented Lagrangian submanifold of $V$ (called the support of the object), $\rho$ is a local system on $L$ (i.e. a complex vector bundle with flat connection), and $\widetilde{Arg}_{L}:L\to{{\bf R}}$ a continuous lift of $Arg_{L}$.

We require that for any element $\beta\in\pi_{2}^{free}(V,L):=\pi_{0}(Maps((D^{2},\partial D^{2}),(V,L))$, the pairing $([\omega],\beta)$ is equal to zero.