Lemma 12.24.4. Let \mathcal{A} be an abelian category. Let \alpha : (K^\bullet , F) \to (L^\bullet , F) be a morphism of filtered complexes of \mathcal{A}. Let (E_ r(K), d_ r)_{r \geq 0}, resp. (E_ r(L), d_ r)_{r \geq 0} be the spectral sequence associated to (K^\bullet , F), resp. (L^\bullet , F). The morphism \alpha induces a canonical morphism of spectral sequences \{ \alpha _ r : E_ r(K) \to E_ r(L)\} _{r \geq 0} compatible with the bigradings.
Proof. Obvious from the explicit representation of the terms of the spectral sequences. \square
Comments (0)
There are also: