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  "body": "\n## Summary\n\nA shelf is a set with a left [[self-distributive operation|VEFE5WZMS3]], that is, a [[magma|9689SFPVE9]] in which each left translation is an endomorphism.\nA [[rack|X74VY86TSX]] is a shelf in which each left translation is a bijection.\nA quandle is a rack in which $x \\triangleright x = x$ for every element $x$.\nShelves that are not racks include the [[Laver tables|9H65YDXMGJ]], which come from set theory, and free shelves, whose study is linked to the braid groups.\n\n## Explanations\n\n### L1 human\n\nIn a shelf, every element $x$ acts on the other elements by $y \\mapsto x \\triangleright y$.\nThe only rule is that this action respects the operation itself: acting with $x$ on $y \\triangleright z$ is the same as letting $x$ act on $y$ and on $z$ first.\nConjugation in a group is the model: conjugating a conjugate is the conjugate of the conjugates.\nA simple example is any set with $x \\triangleright y = y$, where every element acts as the identity.\nUnlike in a rack, the action of an element in a shelf may collapse different elements together.\n",
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    "name": "Shelf",
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        "url": "https://en.wikipedia.org/wiki/Racks_and_quandles"
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    "tag": "PDFC0MRYR8"
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  "name": "Shelf",
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  "source": "https://github.com/tamnd/math2/blob/main/nodes/PDF/PDFC0MRYR8.md",
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        "what": "an inventory row",
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