We introduce the notion of symplectic microfolds and symplectic micromorphisms between them. They form a symmetric monoidal category, which is a version of the “category” of symplectic manifolds and canonical relations obtained by localizing them around Lagrangian submanifolds in the spirit of Milnor’s microbundles.
"Symplectic microgeometry I: micromorphisms." J. Symplectic Geom. 8 (2) 205 - 223, June 2010.