Excisive stabilization

Definition 16.5.3. Let \(C\) be an \(\infty \)-category with finite limits. We denote by \(\Sp ^{\exc }(C)\) the full subcategory \[ \Sp ^{\exc }(C) := \Exc _*(\An _*^{\fin }, C) \subseteq \Fun (\An _*^{\fin }, C) \] spanned by the reduced, excisive functors from \(\An _*^{\fin }\) to \(C\). We denote by \(\Omega ^{\infty }\colon \Sp ^{\exc }(C) \to C\) the evaluation at \(S^0 \in \An _*^{\fin }\).