# Spectral sequence

Jump to navigation
Jump to search

**Spectral sequences** were invented by Jean Leray as an approach to computing sheaf cohomology.

## Historical development

## Definition

A (cohomology) spectral sequence (starting at ) in an abelian category consists of the following data:

- A family of objects of defined for all integers and
- Morphisms that are differentials in the sense that , so that the lines of "slope" in the lattice form chain complexes (we say the differentials "go to the right")
- Isomorphisms between and the homology of at the spot :