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.

中文翻译：

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前代数群的模型论

我们为前代数群的模型理论研究奠定了基础。我们的公理化基于 tannakian 哲学。通过骨架类别的张量模拟，我们能够将具有纤维函子的中性 tannakian 类别视为多排序的一阶结构。详细分析了可对角化的前代数群类。我们证明了可对角化前代数群$G$的理论是由$G$的基域理论和字符群理论决定的。还对类型的综合研究采取了一些初步步骤。