Symplectic category
In mathematics, Weinstein's symplectic category is a category whose objects are symplectic manifolds and whose morphisms are canonical relations, inclusions of Lagrangian submanifolds L into, where the superscript minus means minus the given symplectic form. The notion was introduced by Alan Weinstein, according to whom "Quantization problems 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 without some transversality conditions.
