fuzzy automaton, monad, category theory, language accepted by automaton

The notion of a monadic automaton in a categorywith 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 inputand output morphisms and it is also preserved by morphisms between monads. The proposed framework unifies many of well-known input-output automata types and transformation processes of one type automata to other type.