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  "body": "\n## Example\n\nA [[category|A2DE66937D]] is *small* when its objects and its morphisms form sets.\nThe *category of small categories* $\\mathbf{Cat}$ has the small categories as objects and the [[functors|28NQ0KRHD3]] between them as morphisms.\nThe composite of $F \\colon \\mathcal{A} \\to \\mathcal{B}$ and $G \\colon \\mathcal{B} \\to \\mathcal{C}$ is the functor $G \\circ F$, given on objects and on morphisms by composing the maps.\nThe identity functor of $\\mathcal{A}$ is the identity morphism.\nComposition of functors is associative because it is composition of maps on objects and on morphisms, so $\\mathbf{Cat}$ is a category.\n\n## Remarks\n\nThe empty category is an [[initial object|EK85VSSRMR]], and the category with one object and one morphism is a terminal object.\nThe [[product|S5744QZV4N]] of $\\mathcal{A}$ and $\\mathcal{B}$ is the [[product category|AFNE9C4NH6]] $\\mathcal{A} \\times \\mathcal{B}$.\n$\\mathbf{Cat}$ is [[Cartesian closed|BFBNQ36QS8]]: the exponential object of $\\mathcal{A}$ and $\\mathcal{B}$ is the [[functor category|1X0WKFQX8K]] $\\mathcal{B}^{\\mathcal{A}}$.\nWith [[natural transformations|KYCPCC57FT]] as morphisms between functors, $\\mathbf{Cat}$ becomes a [[2-category|CQACXG10JZ]].\nThe smallness condition avoids a paradox: $\\mathbf{Cat}$ itself is not small, so it is not one of its own objects.\n\n## Explanations\n\n### L1 human\n\nCategories can themselves be the objects of a category, with functors as the arrows between them.\nTo avoid \"the set of all sets\" style problems, one only takes categories whose objects and arrows form sets.\nFor example, a [[monoid|0N6R902FG1]] is a category with one object, and a monoid homomorphism is then exactly a functor, so monoids sit inside $\\mathbf{Cat}$.\n",
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