3 papers
math.CT2026
Pretorsion theories in prenormal categories
Sandra Mantovani, Mariano Messora
In this paper we extend several classical results on pointed torsion theories -- also known as torsion pairs -- to the setting of non-pointed torsion theories defined via kernels a…
math.CT2026
Ideally regular categories
Sandra Mantovani, Mariano Messora
In this note, we propose a generalisation of G. Janelidze's notion of an ideally exact category beyond the Barr exact setting. We define an ideally regular category as a regular, B…
math.CT2025
Prenormal categories
Sandra Mantovani, Mariano Messora
In this paper we introduce the notion of (pointed) prenormal category, modelled after regular categories, but with the key notions of coequaliser and kernel pair replaced by those…