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  "body": "\n## Summary\n\nA (strict) 2-category has objects, morphisms between objects, and 2-morphisms between parallel morphisms.\nThe 2-morphisms compose in two directions, vertically and horizontally, and the two compositions satisfy the interchange law.\nThe main example is the 2-category of small [[categories|A2DE66937D]], [[functors|28NQ0KRHD3]] and [[natural transformations|KYCPCC57FT]].\nFormally, a 2-category is a category [[enriched|BPH9SJ30Y0]] over the category of small categories.\n\n## Explanations\n\n### L1 human\n\nIn a 2-category there are not only arrows between objects, but also arrows between arrows.\nPicture objects as points, morphisms as paths between points, and 2-morphisms as surfaces filling the space between two paths with the same ends.\nSurfaces can be glued along a common path (vertical composition) or side by side at a common point (horizontal composition).\nCategories, functors and natural transformations behave exactly like this: a natural transformation goes from one functor to another.\n",
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