35 citations · 103 across the 24 of their papers we have counts for
6 papers · 1 filter
Spaces of subobjects as spectral spaces
Federico Campanini, Carmelo Antonio Finocchiaro
We study natural topologies on spaces of subobjects of a fixed object in a suitable category, with the aim of determining when these spaces are spectral. A central step in our appr…
A pretorsion theory for right groups
Alberto Facchini, Carmelo Antonio Finocchiaro
Let be a right group. Then there exist two congruences and on such that is the product of its quotient semigroups and , where $S/…
Abstractly constructed prime spectra
Alberto Facchini, Carmelo Antonio Finocchiaro, George Janelidze
The main purpose of this paper is a wide generalization of one of the results abstract algebraic geometry begins with, namely of the fact that the prime spectrum …
A new Galois structure in the category of internal preorders
Alberto Facchini, Carmelo Finocchiaro, Marino Gran
Let be the category of internal preorders in an exact category . We show that the pair $(\mathsf{Eq}(\mathbb C), \mathsf{ParOrd}(\mathbb C))…
Pretorsion theories in general categories
Alberto Facchini, Carmelo Finocchiaro, Marino Gran
We present a setting for the study of torsion theories in general categories. The idea is to associate, with any pair (, ) of full replete subcategories in…
Pretorsion theories, stable category and preordered sets
Alberto Facchini, Carmelo Finocchiaro
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 endow…