category lambda calculus pi calculus Turing machine

objects types structural congruence classes of processes where is the natural numbers and is all binary sequences with finitely many ones.

a morphism an equivalence class of terms a specific reduction from one process state to the next a specific transition from one state and position of the machine to the next

dinatural transformation from the constant functor (mapping to the terminal set and its identity) to a functor generated by hom, products, projections, and exponentials (if they’re there) combinator reduction rule (covers all reductions of a particular form) tape-head update rule (covers all transitions with the current cell and state in common)

products product types parallel processes multiple tapes

internal hom exponential types all types are exponentials? ?