  Quantization problems suggest that the category of symplectic manifolds and
symplectomorphisms be augmented by the inclusion of canonical relations as
morphisms. These relations compose well when a transversality condition is
satisfied, but the failure of the most general compositions to be smooth
manifolds means that the canonical relations do not comprise the morphisms of a
category. We discuss several existing and potential remedies to the
nontransversality problem. Some of these involve restriction to classes of
lagrangian submanifolds for which the transversality property automatically
holds. Others involve allowing lagrangian "objects" more general than
submanifolds.
