In computer science a class of comonads emerges from sets of datastructures with distinguished positions, often equipped with some kind of notion of a neighbourhood of the distinguished position (often called a "focus").

From this perspective a certain functor $C:\mathit{Set}\rightarrow\mathit{Set}$, taking a set to the set of grids of set elements, together with a scheme for applying certain types of locally specified rule over the entire grid, can be considered a comonad. In other words, comonads give a perspective on cellular automata.

See A Categorical Outlook on Cellular Automata by Capobianco and Uustalu for details.

In computer science a class of comonads emerges from sets of datastructures with distinguished positions, often equipped with some kind of notion of a neighbourhood of the distinguished position (often called a "focus").

From this perspective a certain functor $C:\mathit{Set}\rightarrow\mathit{Set}$, taking a set to the set of grids of set elements, together with a scheme for applying certain types of locally specified rule over the entire grid, can be considered a comonad. In other words, comonads give a perspective on cellular automata.

See A Categorical Outlook on Cellular Automata by Capobianco and Uustalu for details.