3 papers
math.CT2026
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…
math.RT2025
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…
math.RA2025
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…