A Type-0 language (in the Chomsky hierarchy) is Turing complete and so you can encode all machines in them - you only need a compiler which translates it to the respective machine code. Appearently, there are categories which also represent programming languages. So how do you encode a programm in a category?
I guess this relates most to functional programming languages. Is (my idea) every machine code equivalent to some morphism? Can I define a category with enough structure such that there a functors to specific categories which equal specific programs? (I see that categories in the theory of computations seem to be used in at least two way, one is related to automata, on to types and monads.)
The question arose when reading cs.stackexchange.com ... is-category-theory-useful-for-learning-functional-programming? and the links there, like the Haskell category tutorial.