Abstract
In this expository paper, we give an explicit construction of an isomorphism between the category of homotopical quantum field theories with an underlying Eilenberg–MacLane space K(G, 1) and the category of G-topological quantum field theories, where G is a finite group. Additionally, in dimension two, we show that there is a monoidal equivalence between the category of G-topological quantum field theories and the category of G-Frobenius algebras.
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