Maslov number $N = 2N_{M\setminus R}$ is a positive multiple of $8$.

7.  $\tilde{J}$ is an $\omega$-compatible almost complex structure on $M$, $\tilde{\omega}$-compatible on $M\setminus R$, and such that $R$ is an almost complex hypersurface for $\tilde{J}$.

8.  Every index zero $\tilde{J}$-holomorphic sphere in $M$, necessarily contained in $R$ by monotonicity, has an intersection number with $R$ equal to a negative multiple of 2.

$\bullet$ The set of morphisms between two objects consists of strings of elementary morphisms $\underline{L} = (L_{01}, L_{12}, \cdots ) $, modulo an equivalence relation:

-   The elementary morphisms are correspondences $L_{i(i+1)} \subset  M_i^- \times M_{i+1}$ which are Lagrangian for the monotone forms $\tilde{\omega}_i$, simply connected, $(R_i, R_{i+1})$-compatible in the sense of Definition \[correspcompat\], such that $L_{i(i+1)} \setminus \left( R_i \times R_{i+1} \right)$ is spin, and such that every pseudo-holomorphic disc of $M_i^- \times M_{i+1}$ with boundary in $L_{i(i+1)}$ and zero area has an intersection number with $(R_i, R_{i+1})$ equal to a positive multiple of $-2$.

-   The equivalence relation on strings of morphisms is generated by the following identification: $(L_{01},\cdots ,  L_{(i-1)i},L_{i(i+1)}, \cdots )$ is identified with $(L_{01},\cdots  L_{(i-1)i}\circ  L_{i(i+1)}, \cdots )$ whenever the composition of $L_{(i-1)i}$ and $L_{i(i+1)}$ is embedded, simply connected, $(R_{i-1} , 