Separable categories (Q1068185)

This paper develops the extension of ring theory to the theory of small additive categories (here called ringoids). Monoid rings are generalized to free additive categories \({\mathbb{Z}}C\) on categories C. The question of separability of \({\mathbb{Z}}C\) is characterized in terms of C. This allows the author to prove a conjecture of \textit{B. Mitchell} [Separable algebroids, Mem. Am. Math. Soc. 333 (1985)] that, for such a C, the category of \({\mathbb{Z}}C\)-modules is equivalent to the product of copies of the category of abelian groups.