On the K-theory of \(\mathbb {Z}\)-categories

Abstract

We establish connections between the concepts of Noetherian, regular coherent, and regular n-coherent categories for \(\mathbb {Z}\)-linear categories with finitely many objects and the corresponding notions for unital rings. These connections enable us to obtain a negative K-theory vanishing result, a fundamental theorem, and a homotopy invariance result for the K-theory of \(\mathbb {Z}\)-linear categories.