  On the one side, the formalism of Global Transformations comes with the claim
of capturing any transformation of space that is local, synchronous and
deterministic.The claim has been proven for different classes of models such as
mesh refinements from computer graphics, Lindenmayer systems from morphogenesis
modeling and cellular automata from biological, physical and parallel
computation modeling.The Global Transformation formalism achieves this by using
category theory for its genericity, and more precisely the notion of Kan
extension to determine the global behaviors based on the local ones.On the
other side, Causal Graph Dynamics describe the transformation of port graphs in
a synchronous and deterministic way and has not yet being tackled.In this
paper, we show the precise sense in which the claim of Global Transformations
holds for them as well.This is done by showing different ways in which they can
be expressed as Kan extensions, each of them highlighting different features of
Causal Graph Dynamics.Along the way, this work uncovers the interesting class
of Monotonic Causal Graph Dynamics and their universality among General Causal
Graph Dynamics.
