Categorification of the ring of cyclotomic integers for products of two primes

TL;DR

This paper constructs a triangulated monoidal category whose Grothendieck ring is isomorphic to the ring of cyclotomic integers for products of two primes, providing a categorification of these algebraic structures.

Contribution

It introduces a new categorification of the ring of cyclotomic integers for products of two primes via a specialized triangulated monoidal category.

Findings

Successfully constructs the desired triangulated monoidal category.

Establishes an isomorphism between the Grothendieck ring and cyclotomic integers.

Provides a new perspective on algebraic structures through categorification.

Abstract

Let $n$ be a product of two distinct prime numbers. We construct a triangulated monoidal category having a Grothendieck ring isomorphic to the ring of $n$:th cyclotomic integers.