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  "body": "\n## Summary\n\nCategory theory is the part of mathematics that studies [[categories|A2DE66937D]], [[functors|28NQ0KRHD3]] between them and [[natural transformations|KYCPCC57FT]] between functors.\nIt describes mathematical structures through the maps between them rather than through their elements.\nIt was introduced by Samuel Eilenberg and Saunders Mac Lane in the 1940s, first to make precise the word \"natural\" in algebraic topology.\nToday it is the common language of algebraic topology, algebraic geometry, homological algebra and parts of logic and computer science.\n\n## Explanations\n\n### L1 human\n\nMany kinds of objects come with their own kind of maps: sets with functions, groups with homomorphisms, spaces with continuous maps.\nCategory theory looks only at the objects, the arrows between them, and how arrows compose.\nFrom this one picture it defines notions that work in every field at once, such as products, isomorphisms and universal properties.\nFor example, the product of two sets, of two groups and of two spaces are all instances of one categorical notion of product.\nA theorem proved at this level holds in every field that fits the picture.\n",
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