In mathematics, Weinstein's symplectic category is (roughly) a category whose objects are symplectic manifolds and whose morphisms are canonical relations, inclusions of Lagrangian submanifolds L into
The notion was introduced by Alan Weinstein, according to whom "Quantization problems[1] suggest that the category of symplectic manifolds and symplectomorphisms be augmented by the inclusion of canonical relations as morphisms."
The composition of canonical relations is given by a fiber product.
Strictly speaking, the symplectic category is not a well-defined category (since the composition may not be well-defined) without some transversality conditions.
This differential geometry-related article is a stub.