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  "body": "\n## Summary\n\nA cohomology operation turns cohomology classes of one fixed degree into classes of another degree.\nIt does so on every space at once, compatibly with all continuous maps.\nExamples are the cup square $x \\mapsto x \\smile x$, the [[Bockstein homomorphism|H7PCM776GR]] and the [[Steenrod squares|VR7RHP41M0]].\nOperations give extra structure on cohomology that can distinguish spaces and maps with the same cohomology groups or rings.\nBy [[representability of cohomology|GPDPYHM3RE]], operations from degree $n$ with coefficients $G$ correspond to cohomology classes of the [[Eilenberg–MacLane space|AJHEYJE5XY]] $K(G, n)$.\n\n## Explanations\n\n### L1 human\n\nCohomology attaches groups to spaces, and maps between spaces give maps between these groups.\nA cohomology operation is a recipe that works on the cohomology of every space and commutes with all these induced maps.\nSquaring a class with the cup product is such a recipe, because induced maps respect cup products.\nOperations are useful because a map must respect them, which can rule out maps that the groups alone allow.\n",
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