Cylindrical consistency is a concept
that allows the embedding of configuration data supported on lattices of graphs
into a continuum configuration space. Loop quantum gravity uses this
concept in order to construct the continuum kinematics from a family of
Here we extend the concept of
cylindrical consistency to the classical and quantum dynamics and argue that
such a dynamics has to be constructed via a coarse graining process. Employing
tensor network renormalization as a method of coarse graining will provide the
embedding maps on which the notion of cylindrical consistency is based.
As an example we will discuss coarse
graining of spin net models, which are lower dimensional analogue models of
spin foams. The dynamics of spin foams is defined by so-called simplicity
constraints and we will argue that the spin net models may already reveal the
behaviour of these simplicity constraints under coarse graining.