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  "body": "\n## Summary\n\nA Galois connection is a pair of maps $f \\colon P \\to Q$ and $g \\colon Q \\to P$ between [[partially ordered sets|011C29Q1S1]] with $f(x) \\le y$ exactly when $x \\le g(y)$.\nIt is a weak form of an order isomorphism, and it is the order-theoretic case of an adjunction between functors.\nThe [[correspondence between subgroups and subfields|R3625YKQC0]] in Galois theory is the classical example, which gives the notion its name.\nEvery Galois connection produces a [[closure operator|17FVAN6HXX]] $g \\circ f$ on $P$.\n\n## Explanations\n\n### L1 human\n\nA Galois connection pairs two ordered sets so that each map is the best approximation to an inverse of the other.\nThe map from integers to reals and the floor function form an example.\nFor an integer $n$ and a real $x$, the statement \"$n \\le x$\" is the same as \"$n \\le \\lfloor x \\rfloor$\".\nSo the floor of $x$ is the best integer approximation of $x$ from below.\n",
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