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

@article{Borceux2022TheSC,
  title={The stable category of preorders in a pretopos II: the universal property},
  author={Francis Borceux and Federico Campanini and Marino Gran},
  journal={Annali di Matematica Pura ed Applicata (1923 -)},
  year={2022}
}
. We prove that the stable category associated with the category PreOrd ( C ) of internal preorders in a pretopos C satisfies a universal property. The canonical functor from PreOrd ( C ) to the stable category Stab ( C ) uni-versally transforms a pretorsion theory in PreOrd ( C ) into a classical torsion theory in the pointed category Stab ( C ). This also gives a categorical insight into the construction of the stable category first considered by Facchini and Finocchiaro in the special case… 

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