Pretorsion theories, stable category and preordered sets

2019/02/14 by Facchini, Alberto, Finocchiaro, Carmelo · 1 citation
#06A06 #06A11 #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.06694

Abstract

We show that in the category of preordered sets, there is a natural notion of pretorsion theory, in which the partially ordered sets are the torsion-free objects and the sets endowed with an equivalence relation are the torsion objects. Correspondingly, it is possible to construct a stable category factoring out the objects that are both torsion and torsion-free.

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• Lattices of pretorsion classes

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