7 citations · 14 across the 8 of their papers we have counts for
5 papers · 1 filter
On coherent systems of subobjects with application to torsion theory
Francis Borceux, Maria Manuel Clementino
In a coherent category, the posets of subobjects have very strong properties. We emphasize the validity of these properties, in general categories, for well-behaved classes of subo…
Groupoids and skeletal categories form a pretorsion theory in
Francis Borceux, Federico Campanini, Marino Gran +1
We describe a pretorsion theory in the category of small categories: the torsion objects are the groupoids, while the torsion-free objects are the skeletal categories, i.e.,…
Pretorsion theories in lextensive categories
Francis Borceux, Federico Campanini, Marino Gran
We propose a construction of a stable category for any pretorsion theory in a lextensive category. We prove the universal property of the stable category, that extends previous res…
The stable category of preorders in a pretopos I: general theory
Francis Borceux, Federico Campanini, Marino Gran
In a recent article Facchini and Finocchiaro considered a natural pretorsion theory in the category of preordered sets inducing a corresponding stable category. In the present work…
The stable category of preorders in a pretopos II: the universal property
Francis Borceux, Federico Campanini, Marino Gran
We prove that the stable category associated with the category of internal preorders in a pretopos satisfies a universal property. The cano…