Introduction to 2-dimensional Topological Quantum Field Theory

TL;DR

This paper provides a self-contained introduction to 2-dimensional Topological Quantum Field Theories, emphasizing category theory, cobordisms, and Frobenius algebras, suitable for beginners and educational purposes.

Contribution

It offers a clear, accessible exposition of the axiomatic framework of 2D TQFTs and proves key equivalences with Frobenius algebras, filling a gap for learners.

Findings

Equivalence of symmetric monoidal functors and commutative Frobenius algebras.

Axiomatic foundation of 2D TQFTs explained with detailed proofs.

Educational material for introductory courses in TQFTs.

Abstract

Mostly self-contained script on functorial topological quantum field theories. These notes give a slow introduction to the basic notions of category theory which serve a closer investigation of cobordisms and (commutative) Frobenius algebras. In the fourth chapter the axiomatic definition of TQFTs is motivated and some folklore results about the equivalence of (symmetric) monoidal functors and (commutative) Frobenius algebras are proven. The script can serve as material for an introductory course.