Symplectic category explained
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
, where the superscript minus means minus the given symplectic form (for example, the graph of a
symplectomorphism; hence, minus). 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.
References
- Notes
Sources
- Weinstein . Alan . Alan Weinstein . 0911.4133 . Symplectic Categories . 2009.
Further reading
See also
Notes and References
- He means geometric quantization.