A categorification of cyclotomic rings

TL;DR

This paper constructs a triangulated monoidal category whose Grothendieck ring precisely matches the cyclotomic integers for any natural number n, providing a categorification of cyclotomic rings.

Contribution

It introduces a new categorical framework that categorifies cyclotomic rings, linking algebraic number theory with higher category theory.

Findings

Established a triangulated monoidal category for each n≥2

Proved the Grothendieck ring is isomorphic to the cyclotomic integers

Bridged algebraic number theory and category theory

Abstract

For any natural number $n \geq 2$, we construct a triangulated monoidal category whose Grothendieck ring is isomorphic to the ring of cyclotomic integers $\mathbb{O}_n$.