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https://en.wikipedia.org/wiki/Grothendieck_spectral_sequence
Grothendieck spectral sequence
(抜粋)
In mathematics, in the field of homological algebra, the Grothendieck spectral sequence, introduced in Tohoku paper, is a spectral sequence that computes the derived functors of the composition of two functors G◯F, from knowledge of the derived functors of F and G.

Contents
1 Examples
1.1 The Leray spectral sequence
1.2 Local-to-global Ext spectral sequence
2 Derivation