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Moore and Segal look at ’equivariant’ TFTs which they equate with Turaev’s HQFTs in his case with background a K(G,1). The term seems a bit strange since the manifolds concerned do not have a G-action, it is just that there are principal G-bundles given on them. Has there been work on the more general case or is that called orbifold TFTs? There seem to be several closely related notions with distinct names and I am getting confused!
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