Sentence:  They act on oscillatory wave functions, whose algebra extends the algebra of formal power series in Planck's constant. In the classical limit, quantum <WSD>microformal</WSD> morphisms reproduce, as the main term of the asymptotic, the nonlinear pullbacks of functions with respect to `classical' <WSD>microformal</WSD> morphisms. 
Meaning of the word marked with <WSD> tags:  "Thickened" using formal canonical relations between the cotangent bundles of smooth manifolds.