I am interested in *Lagrangian correspondences* in the context of symplectic manifolds, namely Lagrangian submanifolds $L_{12}$ of $M_1\times \bar M_2$ where $M_1$ and $M_2$ are symplectic manifolds with symplectic forms $\omega_1$ and $\omega_2$, and $\bar M_2$ has its symplectic form reversed (so the symplectic form on the product is written $\omega_1-\omega_2$, if we omit tedious pullbacks).

As experts know better than I, these correspondences are to be thought of as morphisms in a putative symplectic category. Unfortunately, producing a correspondence $L_{13}$ given correspondences $L_{12}$ and $L_{23}$ is not obvious, unless the latter two intersect transversally.

As of ~10 years ago, there were a few candidate approaches to resolve the issue, which were summarised by Weinstein here:

*Weinstein, Alan*, **Symplectic categories**, Port. Math. (N.S.) 67, No. 2, 261-278 (2010). ZBL1193.53173.

**What is the state of the art today?** Has there been any progress in finding a useful and versatile definition that does not suffer from (as Weinstein calls it) this nontransversality problem?