{
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  "body": "\n## Statement\n\nLet $f \\colon A \\to B$, $g \\colon B \\to C$ and $h \\colon C \\to D$ be [[functions|0XHDTE5YMZ]].\nThen\n$$h \\circ (g \\circ f) = (h \\circ g) \\circ f.$$\n\n## Remarks\n\nBoth sides send each $a \\in A$ to $h(g(f(a)))$, so they are equal.\nBecause of this law, one can write $h \\circ g \\circ f$ without brackets.\nWith the [[identity functions|0FSNQ0GNCC]], the functions from a set to itself form a monoid under composition.\n\n## Explanations\n\n### L1 human\n\nWhen three machines are chained, it does not matter which two you connect first.\nThe input passes through $f$, then $g$, then $h$ in both cases.\n",
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  "name": "Associativity of composition",
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