An exact couple is a mathematical construction used in the context of cohomology and spectral sequences, consisting of two sequences of objects and morphisms that capture the relationship between them. The main goal is to study how these sequences can be manipulated to extract useful algebraic information, particularly about the homological properties of topological spaces or algebraic structures. Exact couples serve as a bridge between homological algebra and the theory of spectral sequences, enabling deeper insights into complex systems.
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