Definition 24.1.7 (Complete Segal anima, Rezk (2001)). A Segal anima \(X\colon \simp \catop \to \An \) is called complete, or is said to satisfy the Rezk condition, if the map \[ X_0 \to X_1^{\sim }, \quad x \mapsto \id _x \] is an equivalence of animae. We denote the full subcategory of complete Segal animae by \(\CSeg (\An ) \subseteq \Seg (\An )\).
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