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刻画任何局部、同步且确定的空间变换。这一主张已在多类模型中得到验证，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耶系统，以及生物、物理和并行计算建模中的元胞自动机。全局变换形式体系通过运用范畴论的通用性——更具体地说是利用Kan扩张概念根据局部行为确定全局行为——实现了这一目标。另一方面，因果图动力学以同步确定的方式描述端口图的变换，但尚未被纳入该框架。本文证明了全局变换主张对因果图动力学同样成立的具体意义，通过展示将其表达为Kan扩张的多种方式实现，每种方式都凸显了因果图动力学的不同特征。在此过程中，本研究揭示了单调因果图动力学这一有趣类别及其在一般因果图动力学中的普适性。