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  "body": "\n## Summary\n\nA heap is a set with a [[ternary operation|WC47MFR6GW]] $[x, y, z]$ that behaves like $x y^{-1} z$ in a [[group|G5S1M9]].\nIt is a group in which no element has been chosen as the identity.\nEvery nonempty heap becomes a group as soon as one element is chosen to play the identity, and the groups for different choices are isomorphic.\nHeaps describe structures without a natural identity, such as the set of bijections between two sets of the same size.\nThey are closely related to [[torsors|5CYEQY4SWR]].\n\n## Explanations\n\n### L1 human\n\nThink of the points of a plane, where nothing marks an origin.\nYou cannot add two points, but from three points $x$, $y$, $z$ you can form $x - y + z$: move $z$ by the arrow that goes from $y$ to $x$.\nA heap keeps exactly this three-point operation.\nFor example, the set of bijections from a set $A$ to a set $B$ is a heap with $[f, g, h] = f \\circ g^{-1} \\circ h$, though there is no natural \"identity bijection\" from $A$ to $B$.\n",
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