Cellular automata and Kan extensions

In this paper, we formalize precisely the sense in which application of a cellular automaton to partial configurations is natural extension its local transition function through categorical notion Kan extension. fact, two possible ways do such an and ingredients involved their definition are related extensions many ways. These relations provide additional links between computer science category theory, also give new point view on famous Curtis–Hedlund theorem automata from extended topological provided by theory. allow relatively easily generalize concepts pioneered arbitrary kinds possibly evolving spaces. No prior knowledge theory assumed for most part.