Definition 12.13.8. Let $\mathcal{A}$ be an abelian category. Let $A^\bullet$ be a cochain complex with boundary maps $d_ A^ n : A^ n \to A^{n + 1}$. For any $k \in \mathbf{Z}$ we identify $H^{i + k}(A^\bullet ) \longrightarrow H^ i(A[k]^\bullet )$ via the identification $A^{i + k} = A[k]^ i$.

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