About categorification of cyclotomic integers and tensored N-complexes

TL;DR

This paper proves that the ideal used for categorifying cyclotomic integers is generated by a cyclotomic polynomial and shows the necessity of enriching the category over cyclotomic integers for tensor products of N-complexes.

Contribution

It establishes the generation of the ideal by a cyclotomic polynomial and confirms the need for enrichment over cyclotomic integers in tensor product categories.

Findings

The ideal in categorification is generated by a cyclotomic polynomial.

Tensor products of N-complexes require enrichment over cyclotomic integers.

Proof by T. Ekedahl supports the necessity of this enrichment.

Abstract

We prove that the ideal used in recent works to categorify the cyclotomic integers is generated by a cyclotomic polynomial. Moreover, we publish a proof by T. Ekedahl that the $q$-binomial relations used in the tensor product of $N$-complexes makes it necessary for the category to be enriched over the cyclotomic integers.