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  "body": "\n## Summary\n\nA free object on a set $X$ is an object generated by $X$ with no relations other than those forced by the axioms.\nIt is defined by a [[universal property|EN4DD2FAJH]]: every map from $X$ into the underlying set of an object extends uniquely to a morphism.\n[[Free groups|0KTW26C80J]], [[free modules|0DZ9DKAKZR]] and [[free monoids|CV013KHVJG]] are the main examples.\nWhen free objects exist on every set, they form a left [[adjoint|TZHF6ZM92S]] of the forgetful functor.\n\n## Explanations\n\n### L1 human\n\nA free object is the most general object you can build from a set of letters.\nIn the free group on $\\set{a, b}$, the elements are words such as $a b a^{-1} b^{-1}$, and no two different reduced words are equal.\nBecause nothing extra holds, you can send $a$ and $b$ to any two elements of any group, and this gives exactly one homomorphism.\nA vector space with basis $X$ is the free vector space on $X$ in the same sense.\n",
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