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  "body": "\n## Summary\n\nA category is made of objects, of morphisms (arrows) between pairs of objects, and of a composition of morphisms that is associative and has identities.\nIt is the basic notion of [[category theory|Q1RZT7DV0F]].\nSets with [[functions|0EPAT51DXQ]], [[groups|G5S1M9]] with [[group homomorphisms|0JYTG5K9Y4]], and [[topological spaces|0CQHFPGJ45]] with [[continuous maps|0VGFHTM75Y]] are categories.\nA category can also be a single structure: a [[monoid|0N6R902FG1]] is a category with one object.\nA [[preorder|0VABYWJWH9]] is a category with at most one morphism between any two objects.\n\n## Explanations\n\n### L1 human\n\nPicture dots for the objects and arrows between them for the morphisms.\nWhenever one arrow ends where another starts, the two can be chained into one arrow.\nChaining is associative, and each dot carries an identity arrow that changes nothing when chained.\nFor example, take as dots the numbers $1, 2, 3$, and draw one arrow from $a$ to $b$ when $a \\le b$.\nArrows chain because $a \\le b$ and $b \\le c$ give $a \\le c$, and the identity arrows come from $a \\le a$.\n",
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