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  "body": "\n## Example\n\nThe *category of sets*, written $\\mathbf{Set}$, has these parts.\nIts objects are all [[sets|0BSJ7RQ9BW]].\nA morphism from $A$ to $B$ is a [[function|0EPAT51DXQ]] $f \\colon A \\to B$.\nComposition is the composition of functions, $(g \\circ f)(a) = g(f(a))$, and the identity of $A$ is the identity function $\\id_A$.\n\nThis is a [[category|A2DE66937D]].\nComposition of functions is associative, since both $(h \\circ g) \\circ f$ and $h \\circ (g \\circ f)$ send $a$ to $h(g(f(a)))$.\nThe identity laws hold, since $f \\circ \\id_A$ and $\\id_B \\circ f$ both send $a$ to $f(a)$.\nThe collection of all sets is not a set, so $\\mathbf{Set}$ is a large category.\nEach hom-set $\\mathbf{Set}(A, B)$ is a set, so $\\mathbf{Set}$ is locally small.\n\n## Remarks\n\nThe empty set is an initial object and every one-point set is a terminal object.\nThe monomorphisms are the [[injective functions|09NWETVTNY]] and the epimorphisms are the [[surjective functions|01RVCMSN5N]].\nProducts are cartesian products and coproducts are disjoint unions; in fact $\\mathbf{Set}$ has all small limits and colimits.\nIt is cartesian closed, with the set of functions $B^A$ as exponential object, and it is an elementary topos whose subobject classifier is a two-element set.\n\n## Explanations\n\n### L1 human\n\nThe category of sets is the most basic category: its objects are sets and its arrows are functions.\nMost other familiar categories, such as groups or topological spaces, are sets with extra structure and functions that respect it.\nMany notions of category theory are modelled on what happens in sets, such as products, unions, images and quotients.\n",
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