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  "body": "\n## Summary\n\nThe Yoneda embedding of a locally small [[category|A2DE66937D]] $\\mathcal{C}$ is a [[functor|28NQ0KRHD3]] into presheaves.\nIt sends each object $A$ to its [[hom functor|VJXS8AK67E]] $\\Hom(-, A)$, a [[presheaf|AND2WHZC8P]] on $\\mathcal{C}$.\nBy the [[Yoneda lemma|D6DF1ARPVD]] it is fully faithful, so $\\mathcal{C}$ is equivalent to a full subcategory of a category of presheaves.\nThis lets one study objects of any category through set-valued functors, where many constructions are easy.\n\n## Explanations\n\n### L1 human\n\nReplace each object $A$ by the record of all arrows that end at $A$, one set for each possible starting object.\nThe Yoneda embedding says that this record loses nothing.\nTwo objects with matching records in a natural way are isomorphic, and arrows between objects are the same as natural maps between their records.\nFor a group $G$ seen as a one-object category, the record of the single object is $G$ itself with $G$ acting by multiplication, and this gives Cayley's theorem.\n",
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