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  "body": "\n## Summary\n\nAn exact couple is a pair of abelian groups with three maps between them that form an exact triangle.\nFrom it one builds a derived exact couple, and repeating this gives a spectral sequence.\nMany spectral sequences of algebraic topology arise in this way.\nExamples are the spectral sequence of a filtered space, the Bockstein spectral sequence and the Adams spectral sequence.\n\n## Explanations\n\n### L1 human\n\nLong exact sequences in topology often come in families, one for each step of a filtration.\nAn exact couple packages such a family into a triangle of two groups and three maps, exact at each corner.\nThe composite of two of the maps squares to zero, so one can take its homology.\nDoing this again and again produces the pages of a spectral sequence.\nFor example, multiplication by a prime $p$ on integral homology and the reduction to mod $p$ homology form an exact couple that gives the Bockstein spectral sequence.\n",
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