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  "body": "\n## Summary\n\nThe Eilenberg–Moore category of a [[monad|FF6XXA6D1A]] $T$ on a category $\\mathcal{C}$ is the category of [[algebras over|QG1ZXRC8EH]] $T$ and their morphisms.\nIt comes with a forgetful functor to $\\mathcal{C}$ and a free algebra functor, and these form an adjunction whose monad is $T$ again.\nIt is the terminal adjunction that gives $T$, and so it shows that every monad comes from an adjunction.\n\n## Explanations\n\n### L1 human\n\nGiven a monad, collect all the ways of evaluating its formal expressions, that is, all its algebras.\nTogether with the maps that respect evaluation, they form a new category.\nFor the list monad on sets, this new category is the category of monoids.\nSo the Eilenberg–Moore category rebuilds an algebraic category from its monad.\n",
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