One contribution from category theory for dealing with stateful systems (like organisms) is the Monad. Monads provide a way to compose together computations into larger ones such that an order of execution can be enforced *and* such that the state doesn't need to be passed around from amongst the functions. Without a design pattern like this, it isn't possible to talk about the interactions of a complex set of objects and their internal changes without allowing side-effects (which will mean the functions aren't really functions in the mathematical sense), or exposing irrelevant and often complex internal state in the equation parameters.
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