Shelf

Summary

A shelf is a set with a left self-distributive operation, that is, a magma in which each left translation is an endomorphism. A rack is a shelf in which each left translation is a bijection. A quandle is a rack in which $x \triangleright x = x$ for every element $x$. Shelves that are not racks include the Laver tables, which come from set theory, and free shelves, whose study is linked to the braid groups.