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  "body": "\n## Summary\n\nIn a locally small [[category|A2DE66937D]] $\\mathcal{C}$, each object $A$ gives a [[functor|28NQ0KRHD3]] $\\Hom(A, -)$ from $\\mathcal{C}$ to the category of sets.\nIt sends an object $X$ to the set of morphisms $A \\to X$.\nDually, $\\Hom(-, A)$ is a contravariant functor.\nHom functors are the basic examples of functors into sets, and the Yoneda lemma says that they control all other such functors.\n\n## Explanations\n\n### L1 human\n\nAn object $A$ can be studied by the arrows that leave it: for each object $X$, collect all arrows from $A$ to $X$ into a set.\nAn arrow $X \\to Y$ then turns each arrow $A \\to X$ into an arrow $A \\to Y$, by following one and then the other.\nThis turns $\\Hom(A, -)$ into a functor.\nFor example, in the category of sets with $A = \\{*\\}$ a one-point set, a map $\\{*\\} \\to X$ is the same as a point of $X$, so $\\Hom(\\{*\\}, -)$ is essentially the identity functor.\n",
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