  Using convex Grothendieck fibrations, we characterize the von Neumann entropy
as a functor from finite-dimensional non-commutative probability spaces and
state-preserving *-homomorphisms to real numbers. Our axioms reproduce those of
Baez, Fritz, and Leinster characterizing the Shannon entropy difference. The
existence of disintegrations for classical probability spaces plays a crucial
role in our characterization.
