Left and Right Kan Extensions in Cellular Automata

Paraphrasing the famous book of Saunders Mac Lane: “Everything is a Kan Extension”. However, depending on ones background of course, there might not be many examples that arise directly as Kan Extensions. In this talk, we show how the latter describes very naturally local to global definitions, as is the case for cellular automata for instance. Indeed the formal definition simply says “you have a local transformation and a way to compare arbitrary transformations? So simply choose the best global transformation possible !”.
This is based on my works with Antoine Spicher and Alexandre Fernandez on so-called “Global Transformations