Evaluation 2-Functors for Kac-Moody 2-Categories of Type A2

TL;DR

This paper constructs a 2-functor linking Kac-Moody 2-categories of types A2, providing a categorification of the evaluation map between quantum Kac-Moody algebras, advancing the understanding of their higher categorical structures.

Contribution

It introduces a new 2-functor from the Kac-Moody 2-category for extended quantum affine sl(3) to a homotopy 2-category, categorifying the evaluation map between related quantum algebras.

Findings

Constructed a 2-functor for type A2 Kac-Moody categories.

Categorified the evaluation map between quantum Kac-Moody algebras.

Enhanced the understanding of higher categorical structures in quantum algebra.

Abstract

We construct a 2-functor from the Kac-Moody 2-category for the extended quantum affine sl(3) to the homotopy 2-category of bounded chain complexes with values in the Kac-Moody 2-category for quantum gl(3), categorifying the evaluation map between the corresponding quantum Kac-Moody algebras.