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

2022/01/20 by Borceux, Francis, Campanini, Federico, Gran, Marino
#06A75 #18B25 #18B35 #18B50 #18E08 #18E40 #Category Theory (math.CT) #FOS: Mathematics #Logic (math.LO) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2201.08016

Abstract

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

Related

• Pretorsion theories, stable category and preordered sets
• Pretorsion theories in lextensive categories
• The stable category of preordered groups
• A pretorsion theory for the category of all categories
• Building pretorsion theories from torsion theories