the correspondence from $M'$ to $M$, obtained by reversing the arrows.

We will denote $pt$ the symplectic manifold consisting of one point. A Lagrangian correspondence from $pt$ to $M$ is then simply a Lagrangian submanifold of $M$.

If $\underline{L}$ is a generalized Lagrangian correspondence from $pt$ to $pt$, the quilted Floer homology of $\underline{L}$ can be defined (whenever this is possible) as the Lagrangian Floer homology $$HF(\underline{L}) = HF( L_{01}\times L_{23} \times \cdots , L_{12}\times L_{34} \times \cdots ),$$ where the ambient symplectic manifold is the product of all the manifolds $M_0^- \times M_1 \times M_2^- \times \cdots $. When $L_{01}\times L_{23} \times \cdots $ and $L_{12}\times L_{34} \times \cdots $ intersect transversely, the corresponding chain complex is generated by the set of *generalized intersection points* $${\mathcal{I}}(\underline{L}) =\lbrace (x_0, \cdots , x_k) ~|~ \forall i, (x_i,x_{i+1}) \in L_{i(i+1)}   \rbrace,$$ and its differential counts index 1 Floer trajectories, which can alternatively be viewed as “quilted strips”. We now recall the definition of quilted surface and pseudo-holomorphic quilt, which are the key objects involved in Wehrheim and Woodward’s theory:

A *quilted surface* $\underline{S}$ consists of:

1.  a collection of Riemann surfaces $\underline{S} = (S_k)_{k=1\cdots m}$, called patches, and endowed with complex structures 