Homology Spectral Sequence
Similarly to the cohomology spectral sequence, there is one for homology:
where the notations are dual to the ones above.
It is actually a special case of a more general spectral sequence, namely the Serre spectral sequence for fibrations of simplicial sets. If f is a fibration of simplicial sets (a Kan fibration), such that π1(B) the first homotopy group of the simplicial set B, vanishes, there is a spectral sequence exactly as above. (Applying the functor which associates to any topological space its simplices to a fibration of topological spaces, one recovers the above sequence).
Read more about this topic: Serre Spectral Sequence
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