Equivariant Topological Quantum Field Theory in Dimension 2

TL;DR

This paper provides a detailed proof of the equivalence between 2D G-equivariant topological quantum field theories and G-Frobenius algebras, extending prior results by Moore and Segal.

Contribution

It offers a comprehensive and detailed proof of the monoidal equivalence between G-equivariant TQFTs and G-Frobenius algebras in dimension 2.

Findings

Establishes the monoidal equivalence in dimension 2

Provides detailed proof of the equivalence

Clarifies the structure of G-equivariant TQFTs

Abstract

For $G$ a finite group, we prove in dimension 2 that there is a monoidal equivalence between the category of $G$-equivariant topological quantum field theories and the category of $G$-Frobenius algebras, this was proved by G. Moore and G. Segal. This work consists to give, in more detail, a proof of this result.