  The decomposition into interaction subspaces is an important result for
graphical models and plays a central role for results on the linearized
marginal problem; similarly the Chaos decomposition plays an important role in
statistical physics at the thermodynamic limit and in probability theory in
general. We unify and extend both constructions by defining and characterizing
decomposable functors from a well-founded poset to the category of Hilbert
spaces, completing previous work on decomposable collections of vector
subspaces and presheaves.
