  We construct a special class of semiclassical Fourier integral operators
whose wave fronts are symplectic micromorphisms. These operators have very good
properties: they form a category on which the wave front map becomes a functor
into the cotangent microbundle category, and they admit a total symbol calculus
in terms of symplectic micromorphisms enhanced with half-density germs. This
new operator category encompasses the semi-classical pseudo-differential
calculus and offers a functorial framework for the semi-classical analysis of
the Schr\"odinger equation. We also comment on applications to classical and
quantum mechanics as well as to a functorial and geometrical approach to the
quantization of Poisson manifolds.
