Definition 12.22.5. Let $\mathcal{A}$ be an abelian category. Let $(A, d)$ be a differential object of $\mathcal{A}$. Let $\alpha : A \to A$ be an injective selfmap of $A$ which commutes with $d$. The *spectral sequence associated to $(A, d, \alpha )$* is the spectral sequence $(E_ r, d_ r)_{r \geq 0}$ described above.

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