  According to Jae Suk Park, physicists use "canonical coordinate systems" to
compute correlations in perturbative quantum field theories. One may interpret
these canonical coordinate systems as equivalences of generalized differential
Lie algebras. In this note we discuss these flattenings in one particular
setting and refer to them as "cumulant bijections". The main point we make is
that these cumulant bijections are functorial for deformation retracts. The
discussion is completely self contained and based on well known universal
properties.
