The stable category of preorders in a pretopos II: the universal property

Abstract

We prove that the stable category associated with the category $\mathsf{PreOrd}(\mathbb{C})$ of internal preorders in a pretopos $\mathbb{C}$ satisfies a universal property. The canonical functor from $\mathsf{PreOrd}(\mathbb{C})$ to the stable category $\mathsf{Stab}(\mathbb{C})$ universally transforms a pretorsion theory in $\mathsf{PreOrd}(\mathbb{C})$ into a classical torsion theory in the pointed category $\mathsf{Stab}(\mathbb{C})$. This also gives a categorical insight into the construction of the stable category first considered by Facchini and Finocchiaro in the special case when $\mathbb{C}$ is the category of sets.

22 pages, some minor corrections have been made