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Cellular Automata and Kan Extensions Fernandez, Alexandre Maignan, Luidnel Spicher, Antoine Cellular Automata Kan Extension Category Theory Global Transformation 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 view on the famous Curtis-Hedlund theorem of cellular automata from the extended topological point of view provided by category theory. These links also allow to relatively easily generalize concepts pioneered by cellular automata to arbitrary kinds of possibly evolving spaces. No prior knowledge of category theory is assumed. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Alexandre Fernandez and Luidnel Maignan and Antoine Spicher 2021 Is Part Of OASIcs, Volume 90, 27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/OASIcs.AUTOMATA.2021.7 urn:nbn:de:0030-drops-140160 https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.AUTOMATA.2021.7 eng https://creativecommons.org/licenses/by/4.0/legalcode