Work

A 2-dimensional torsion theory on symmetric monoidal categories

Year: 2025

Type: article

Abstract: In this paper, we describe a homotopy torsion theory on the category of small symmetric monoidal categories. By using natural isomorphisms as the basis for the nullhomotopy structure, this homotopy torsion theory exhibits some interesting 2-dimensional properties which could be the foundation for a definition of “2-dimensional torsion theory”. We choose symmetric 2-groups as torsion objects, thereby generalising a known pointed torsion theory in the category of commutative monoids where abelian groups are taken as torsion objects. In the final part of the paper we carry out an analogous generalisation for the classical torsion theory in the category of abelian groups given by torsion and torsion-free abelian groups.

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2025.04.014

Author: Mariano Messora

Institution: University of Milan

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,310

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni