4 papers
Categorical Algebra of Atomic Monoids: Presentability, Regularity, and Pretorsion Theories
Federico Campanini, Laura Cossu
We study the category of atomic monoids and atom-preserving homomorphisms. We prove that is locally finitely presentable by exhibiting a strong…
Lattices of pretorsion classes
Federico Campanini, Francesca Fedele, Emine Yıldırım
Since their introduction, torsion theories have played a key role in the study of abelian and pointed categories. In representation theory, torsion theories and lattices of torsion…
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties
Federico Campanini, Laura Cossu, Salvatore Tringali
We introduce and investigate the category of atomic monoids and atom-preserving monoid homomorphisms, which is a (non-full) subcategory of the usual category of m…
Building pretorsion theories from torsion theories
Federico Campanini, Francesca Fedele
Torsion theories play an important role in abelian categories and they have been widely studied in the last sixty years. In recent years, with the introduction of pretorsion theori…