7 citations · 14 across the 8 of their papers we have counts for
8 papers
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…
On the representability of actions in the topos context
Francis Borceux
The notion of a group G acting on a group X is well-known. Fixing X, the corresponding functor Act(-,X) is representable by the group [X] of automorphisms of X. The notion of G-act…
Monadic approach to Galois descent and cohomology
F. Borceux, S. Caenepeel, G. Janelidze
We describe a simplified categorical approach to Galois descent theory. It is well known that Galois descent is a special case of Grothendieck descent, and that under mild addition…
On closure operators and reflections in Goursat categories
Francis Borceux, Marino Gran, Sandra Mantovani
By defining a closure operator on effective equivalence relations in a regular category , it is possible to establish a bijective correspondence between these closure operators…