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  "body": "\n## Summary\n\nAn algebra over a [[monad|FF6XXA6D1A]] $T$ on a category $\\mathcal{C}$ is an object $A$ with a structure map $a \\colon T(A) \\to A$.\nThe structure map must be compatible with the unit and the multiplication of $T$.\nThese algebras, with the maps that respect the structure maps, form the Eilenberg–Moore category of $T$.\nMany algebraic structures are algebras over a monad on sets.\nExamples are monoids for the list monad, complete join-semilattices for the power set monad, and modules for the free module monad.\n\n## Explanations\n\n### L1 human\n\nA monad describes formal expressions, and an algebra is a way to evaluate them.\nThe structure map $a$ takes a formal expression in elements of $A$ and returns an element of $A$.\nThe first law says that evaluating a single element gives back that element.\nThe second law says that evaluating in stages gives the same result as flattening first and evaluating once.\nFor the list monad, a monoid $M$ is an algebra: a list $(m_1, \\dots, m_n)$ evaluates to the product $m_1 \\cdots m_n$.\n",
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