Spectral Sequence

An algebraic tool that organizes successive approximations to the homology or cohomology of a filtered complex by means of a family of pages E_r and differentials d_r; each page is a bigraded object whose later pages are the homology of earlier pages and whose limit (when it exists) yields the graded pieces of the target group's associated graded object.

An iterative computational framework that organizes successive approximations to (co)homology or homotopy-type invariants via a sequence of pages E_r and differentials d_r, whose abutment and E_∞ page determine graded pieces of the target invariant up to extension information.