  We lay the foundations for a model theoretic study of proalgebraic groups.
Our axiomatization is based on the tannakian philosophy. Through a tensor
analog of skeletal categories we are able to consider neutral tannakian
categories with a fibre functor as many-sorted first order structures. The
class of diagonalizable proalgebraic groups is analyzed in detail. We show that
the theory of a diagonalizable proalgebraic group $G$ is determined by the
theory of the base field and the theory of the character group of $G$. Some
initial steps towards a comprehensive study of types are also made.
