arXiv 2201.080162022-01math.CTmath.LOmath.RA

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

Francis Borceux, Federico Campanini, Marino Gran

备注：: 22 pages, some minor corrections have been made

英文摘要：

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.

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