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  "body": "\n## Summary\n\nA monoidal category is a [[category|A2DE66937D]] with a tensor product of objects and a unit object, associative and unital up to coherent isomorphism.\nIt is the categorical version of a [[monoid|0N6R902FG1]], one level up.\nSets with the Cartesian product, vector spaces with the [[tensor product|0BF2DE2SYK]], and endofunctors with composition are monoidal categories.\nMonoidal categories are the setting for monoid objects, enriched categories, duals, and the string diagrams of quantum algebra and computer science.\n\n## Explanations\n\n### L1 human\n\nA monoidal category is a category where two objects can be put side by side to give a new object.\nPutting $A$ next to $B$, and then next to $C$, gives the same result as putting $A$ next to the pair $B, C$, but only up to a chosen isomorphism.\nThere is also an \"empty\" object $I$ that changes nothing when placed next to another.\nFor example, for sets the product $A \\times B$ is the side-by-side object, and a one-point set is the empty object, since $\\set{*} \\times A$ is in bijection with $A$.\n",
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