ABSTRACT
Automata defined by monads in categories are introduced as special examples of monoids actions on free -algebras, where
is a monad in a category. Morphisms between monads are introduced as special functors between Kleisli categories. Any morphism generates a functor between the corresponding categories of monadic automata. The relationship between morphisms of monads and functors of corresponding monadic automata categories gives a common framework in the theory of automata defined by monads. The proposed framework unifies many of well-known automata types and transformation processes of one type automata to other type. The notion of a monadic automaton with input and output morphisms, and a language accepted by this monadic automaton are introduced. An acceptance of a language is preserved by morphisms between monadic automata with input and output morphisms and it is also preserved by morphisms between monads.
Disclosure statement
No potential conflict of interest was reported by the author.