Definition 12.25.2. Let $\mathcal{A}$ be an abelian category. Let $K^{\bullet , \bullet }$ be a double complex. We say the spectral sequence $({}'E_ r, {}'d_ r)_{r \geq 0}$ weakly converges to $H^ n(\text{Tot}(K^{\bullet , \bullet }))$, abuts to $H^ n(\text{Tot}(K^{\bullet , \bullet }))$, or converges to $H^ n(\text{Tot}(K^{\bullet , \bullet }))$ if Definition 12.24.9 applies. Similarly we say the spectral sequence $({}''E_ r, {}''d_ r)_{r \geq 0}$ weakly converges to $H^ n(\text{Tot}(K^{\bullet , \bullet }))$, abuts to $H^ n(\text{Tot}(K^{\bullet , \bullet }))$, or converges to $H^ n(\text{Tot}(K^{\bullet , \bullet }))$ if Definition 12.24.9 applies.

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