An exact couple is a mathematical construct that arises in the study of homological algebra, particularly in the context of spectral sequences. It consists of two chain complexes and a series of maps between them that satisfy certain exactness conditions, allowing one to derive information about homology groups. Exact couples are crucial in organizing data for the construction of spectral sequences, such as the Serre spectral sequence and the Čech-to-derived functor spectral sequence.
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