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Homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.
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spectral sequence for a complex with two filtrations
It induces a filtration on the homology of $C$ (a complex with zero differential),
$0= H_0 \subseteq H_1 \subseteq \cdots \subseteq H(C,d)$. …