Remark 1.4.26. The condition that the functor \(i\colon C \to \Iso (C)\) is an equivalence is known as the completeness condition. It was used by Rezk [Rezk (2001)] to provide a model of \(\infty \)-categories, called complete Segal spaces. A detailed discussion of the equivalence between \(\infty \)-categories and complete Segal animae will be given in Chapter 24.
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