Title
The Freyd--Schützenberger completion of a small category
Abstract
The Schützenberger category of a monoid, or more generally of a small category, extends its Cauchy completion by splitting universally each morphism as an epimorphism followed by a monomorphism, instead of just the idempotents. After giving a concrete description, we will see how the Green--Rees local structure of finite monoids emerges from this construction when it is applied to a monoid seen as a category with one object.
