Cellular Automata and Kan Extensions

@article{Fernandez2021CellularAA,
  title={Cellular Automata and Kan Extensions},
  author={Alexandre Fernandez and Luidnel Maignan and Antoine Spicher},
  journal={ArXiv},
  year={2021},
  volume={abs/2102.12156}
}
In this paper, we formalize precisely the sense in which the application of a cellular automaton to partial configurations is a natural extension of its local transition function through the categorical notion of Kan extension. In fact, the two possible ways to do such an extension and the ingredients involved in their definition are related through Kan extensions in many ways. These relations provide additional links between computer science and category theory, and also give a new point of… Expand
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