Heap

Summary

A heap is a set with a ternary operation $[x, y, z]$ that behaves like $x y^{-1} z$ in a group. It is a group in which no element has been chosen as the identity. Every nonempty heap becomes a group as soon as one element is chosen to play the identity, and the groups for different choices are isomorphic. Heaps describe structures without a natural identity, such as the set of bijections between two sets of the same size. They are closely related to torsors.