1 citations · 2 across the 6 of their papers we have counts for
6 papers
Conservative functors to pointed categories
Sandra Mantovani, Mariano Messora
Many results in categorical algebra rely fundamentally on pointedness, yet numerous categories of mathematical interest are not pointed. Building on ideas from the theory of ideall…
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…
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…
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…
A 2-dimensional torsion theory on symmetric monoidal categories
Mariano Messora
In this paper we describe a homotopy torsion theory in the category of small symmetric monoidal categories. Thanks to the use of natural isomorphisms as basis for the nullhomotopy…
Homotopy torsion theories
Sandra Mantovani, Mariano Messora, Enrico M. Vitale
In the context of categories equipped with a structure of nullhomotopies, we introduce the notion of homotopy torsion theory. As special cases, we recover pretorsion theories as we…