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  "body": "\n## Summary\n\nAn exponential object $Z^Y$ in a category with [[products|S5744QZV4N]] is an object of morphisms from $Y$ to $Z$, together with an evaluation morphism.\nIt is defined by a [[universal property|EN4DD2FAJH]] that expresses currying: maps $X \\times Y \\to Z$ match maps $X \\to Z^Y$.\nExponential objects are the defining feature of [[Cartesian closed categories|BFBNQ36QS8]].\nThey give the semantics of function types in [[lambda calculus|BD756KR8FM]].\n\n## Explanations\n\n### L1 human\n\nA function of two variables $g(x, y)$ can be seen as a function of $x$ whose values are functions of $y$.\nThis trick is called currying.\nFor sets, the exponential $Z^Y$ is the set of all functions from $Y$ to $Z$.\nFor example, if $Y$ has $2$ elements and $Z$ has $3$, then $Z^Y$ has $3^2 = 9$ elements.\nAn exponential object is the same idea in any category with products.\n",
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