Shifted infinite loop anima functors

Definition 4.3.24. Let \(C\) be an \(\infty \)-category with finite limits. For \(n \geq 0\), define \[ \Omega ^{\infty - n} \colon \Sp (C) \to C_*, \qquad \qquad \Omega ^{\infty - n}(X) := \Omega ^{\infty }(X[n]), \] where \(X[n]\) denotes the \(n\)-fold suspension of \(X\) in the stable \(\infty \)-category \(\Sp (C)\). By Corollary 4.3.15, this functor evaluates at the \(n\)-th level in the prespectrum model: \(\Omega ^{\infty - n}(X) \simeq X_n\).