A Note on the categorification of Lie algebras

TL;DR

This paper explores how Lie algebras can be understood within symmetric monoidal categories, reviewing existing work, presenting new examples, and analyzing functors that preserve Lie algebra structures.

Contribution

It provides a review of Lie algebra categorification, introduces new examples, and investigates functors that maintain Lie algebra structures in monoidal categories.

Findings

Identifies conditions under which functors preserve Lie algebra structures.

Provides new examples of Lie algebras in symmetric monoidal categories.

Summarizes existing approaches to categorification of Lie algebras.

Abstract

In this short note we study Lie algebras in the framework of symmetric monoidal categories. After a brief review of the existing work in this field and a presentation of earlier studied and new examples, we examine which functors preserve the structure of a Lie algebra.