Determinization, an algebraic approach

The algebraic approach to recognizability has been proposed since the 1960s and an instance of non-determinism can be formulated by means of direct images of homomorphisms. In this talk, I will present the general problem of determinization from an algebraic and categorical perspective by using monads. I will present some sufficient conditions in which direct images of recognizable languages are recognizable and show an example in which this property does not hold. The general problem to characterize this property is still open. I will conclude the talk with some open questions and related problems.