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.

翻译：一方面，全局变换形式体系声称能够捕捉任何局域、同步且确定性的空间变换。该声称已在不同模型类中得到证明，包括计算机图形学中的网格细化、形态发生建模中的林登迈尔系统，以及生物、物理与并行计算建模中的元胞自动机。全局变换形式体系通过使用范畴论实现通用性，更精确地说，利用Kan扩展的概念基于局域行为确定全局行为。另一方面，因果图动态以同步且确定性的方式描述端口图变换，目前尚未被解决。本文展示了全局变换声称同样适用于因果图动态的精确含义。具体而言，我们通过展示因果图动态可被表达为Kan扩展的不同方式来实现这一目标，每种方式均凸显了因果图动态的不同特征。在此过程中，本研究揭示了单调因果图动态这一有趣类别及其在一般因果图动态中的普适性。