The notion of spectral sequence is an algorithm or computational tool in homological algebra and more generally in homotopy theory which allows to compute chain homology groups/homotopy groups of bi-graded objects from the homology/homotopy of the two graded components. Notably there is a spectral sequence for computing the homology of the total complex of a double complex from the homology of its row and column complexes separately. This in turn allows to compute derived functors of composite..