Proposition 4.3.16. For an \(\infty \)-category \(C\) with finite limits, the functor \(\Omega ^{\infty }\colon \Sp (C) \to C\) exhibits \(\Sp (C)\) as a stabilization of \(C\).
Proof. The proof of Theorem 4.3.14 gives a natural isomorphism \(\id _{\Sp (C)} \cong \Omega \circ \shift \). Since \(\Sigma \) is inverse to \(\Omega \), this identifies \(\Sigma \) with \(\shift \). □
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