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  "body": "\n## Summary\n\nA commutative diagram is a drawing of objects and [[morphisms|859F0TFVA3]] of a [[category|A2DE66937D]].\nIn it, any two directed paths with the same start and the same end compose to the same morphism.\nDiagrams are the main notation of category theory and homological algebra: one picture records many equations between composites.\nThe commutative square $g \\circ f = k \\circ h$ and the commutative triangle $g \\circ f = h$ are the basic shapes.\nThe definition of a [[natural transformation|KYCPCC57FT]] is the commutativity of one square for each morphism.\n\n## Explanations\n\n### L1 human\n\nDraw objects as points and morphisms as arrows between them.\nFollowing a path of arrows means composing them.\nThe diagram commutes if any two routes from one point to another give the same result.\nFor example, with $f(x) = x + 1$ and $g(x) = 2x$ on the real numbers, the square \"first $f$ then $g$\" against \"first $g$ then $f$\" does not commute.\nThe first route gives $2x + 2$ and the second gives $2x + 1$.\n",
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