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Bibliographic Details
Main Author: Elgueta, Josep
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2604.10154
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author Elgueta, Josep
author_facet Elgueta, Josep
contents By a 2-ring we mean a groupoid with a structure analogous to that of a ring, up to coherent isomorphisms. Two different notions of 2-ring appear in the literature: the notion of {\em Ann-category}, due to Quang, and the notion of {\em categorical ring}, due to Jibladze and Pirashvili. The underlying data are the same in both cases, but the required axioms differ. In this note, we clarify the relationship between these notions by explaining why an additional axiom must be imposed for the two notions to be equivalent. Essential to this analysis is an equivalent description of a symmetric monoidal category.
format Preprint
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institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On the (algebraic) notion of 2-ring
Elgueta, Josep
Category Theory
By a 2-ring we mean a groupoid with a structure analogous to that of a ring, up to coherent isomorphisms. Two different notions of 2-ring appear in the literature: the notion of {\em Ann-category}, due to Quang, and the notion of {\em categorical ring}, due to Jibladze and Pirashvili. The underlying data are the same in both cases, but the required axioms differ. In this note, we clarify the relationship between these notions by explaining why an additional axiom must be imposed for the two notions to be equivalent. Essential to this analysis is an equivalent description of a symmetric monoidal category.
title On the (algebraic) notion of 2-ring
topic Category Theory
url https://arxiv.org/abs/2604.10154