is said to be a chain complex (or -complex, or just complex) if each pair of adjacent homomorphisms
satisfies the relation
. This is equivalent to saying that
. We often denote such a complex by
, or simply .
Compare this to the notion of an exact sequence, which requires
.
The homomorphisms in the chain complex are called boundary operators, or boundary maps.
This is version 9 of chain complex, born on 2002-01-05, modified 2008-03-18.
Object id is 1353, canonical name is ChainComplex.
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