A categoricity property of the Poincare fundamental groupoid functor

I will try to argue that model theoretic critetia may be useful in the analysis of the structures apprearing in category theory, and that, in particular, somtimes the model-theoretic notion of categoricity can be phrased in the language of category theory. I will do so on the example of the Poincare fundamental groupoid functor : the model theoretic analyis leads to conjecture a uniqueness (universality) property of this functor considered on a subcategory of the category of algebraic varieties; the techniques of model theory allow us to prove the result by reducing it to several facts of algebraic geometry.