Thank you! This is the concept I've been looking for. I always had the sense that compositional data transformation frameworks like PRQL or LINQ should have a clean categorical interpretation. I was exploring how this could be expressed in terms of monads but they usually start with the data while I was trying to formalise the composition of the transformations. I think transducers are it.

Transducers are just the morphisms in the category of the reducing-functions. No problem!