Linear relations over commutative rings

Abstract

We consider the category of linear relations over an arbitrary commutative ring, and identify it as a subcategory of the category of Kronecker representations. We observe that this subcategory forms a definable, faithful and hereditary torsion-free class. We also generalise results used in the functorial filtrations method, known before only in case the ground ring is a field. In particular, our results strictly generalise what the so-called the `covering' and `splitting' properties from this method.