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Deleted the following fragment, since the erratum points out that what is being constructed is categories with involution, not groupoids:
Model category presentations of groupoid objects in ∞Grpd by groupoidal complete Segal spaces are discussed in
Adding inverses to diagrams encoding algebraic structures, Homology, Homotopy and Applications 10 (2008), no. 2, 149–174. (arXiv:0610291)
Adding inverses to diagrams II: Invertible homotopy theories are spaces, Homology, Homotopy and Applications, Vol. 10 (2008), No. 2, pp.175-193. (web, arXiv:0710.2254)
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