Definition 4.2.10 (Shift functors). For \(n \in \mathbb {Z}\), we define the \(n\)-th shift functor \([n]\colon C \to C\) by \[ [n] := \begin {cases} \Sigma ^n & \text {if } n \geq 0 \\ \Omega ^{-n} & \text {if } n \leq 0 \end {cases}. \] The two formulas agree for \(n=0\).
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