# Parameters in categorified quantum groups

## TL;DR

This paper establishes explicit isomorphisms between different versions of categorified quantum groups related to simply-laced Kac-Moody algebras, facilitating translation of results across variants and conventions.

## Contribution

It provides explicit 2-category isomorphisms between various categorified quantum groups and extends isomorphisms of finite type KLR algebras to the 2-category level.

## Key findings

- Explicit isomorphisms between categorified quantum groups for simply-laced Kac-Moody algebras.
- Ability to transfer results between gl(n) and sl(n) variants.
- Extension of KLR algebra isomorphisms to 2-categories.

## Abstract

In this note we give explicit isomorphisms of 2-categories between various versions of the categorified quantum group associated to a simply-laced Kac-Moody algebra. These isomorphisms are convenient when working with the categorified quantum group. They make it possible to translate results from the gl(n) variant of the 2-category to the sl(n) variant and transfer results between various conventions in the literature. We also extend isomorphisms of finite type KLR algebras for different choices of parameters to the level of 2-categories.