Spectrum objects as a limit

Remark 4.3.5. Assume \(C\) is a small \(\infty \)-category. Then the structure maps \(\sigma _n \colon (-)_n \iso \Omega (-)_{n+1}\) turn the functors \((-)_{n}\colon \Sp (C) \to C_*\) into a cone in \(\Cat _{\infty }\), resulting in a comparison functor \[ \Sp (C) \to \lim ( \dots \to C_* \xrightarrow {\Omega } C_* \xrightarrow {\Omega } C_*). \] This functor is an equivalence of \(\infty \)-categories.