# Introductory lectures on topological quantum field theory

## TL;DR

This paper provides an accessible introduction to topological quantum field theory, emphasizing the functorial axiomatization, algebraic formulations, and the relation to braided monoidal categories, suitable for newcomers.

## Contribution

It offers a simplified, algebraic perspective on TQFTs, connecting path integral ideas with categorical frameworks, and discusses extended TQFTs in three dimensions.

## Key findings

- Finite algebraic data for 1- and 2-dimensional TQFTs
- 3-dimensional TQFTs require infinite data
- Extended 3D TQFTs relate to braided monoidal categories

## Abstract

These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the definition in terms symmetric monoidal categories, and we highlight the algebraic formulation emerging from a formal generators-and-relations description. This allows one to understand (oriented, closed) 1- and 2-dimensional TQFTs in terms of a finite amount of algebraic data, while already the 3-dimensional case needs an infinite amount of data. We evade these complications by instead discussing some aspects of 3-dimensional extended TQFTs, and their relation to braided monoidal categories.