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

We prove that the stable category associated with the category (ℂ) of internal preorders in a pretopos ℂ satisfies a universal property. The canonical functor from (ℂ) to the stable category (ℂ) universally transforms a pretorsion theory in (ℂ) into a classical torsion theory in the pointed category (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 ℂ is the category of sets