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  "body": "\n## Summary\n\nA monoid object in a [[monoidal category|M3MSQ3NKAE]] is an object $M$ with a multiplication $M \\otimes M \\to M$ and a unit $I \\to M$.\nThese must satisfy the associativity and unit laws, written as equations between morphisms.\nIt generalizes the notion of a [[monoid|0N6R902FG1]] to any monoidal category.\nMonoids in sets are ordinary monoids, monoids in abelian groups are [[rings|0B1261B5ED]], monoids in vector spaces are associative algebras, and monoids among endofunctors are [[monads|FF6XXA6D1A]].\nMany algebraic structures are thus one notion read in different monoidal categories.\n\n## Explanations\n\n### L1 human\n\nA monoid is a set with an associative multiplication and a unit, like the whole numbers under addition.\nA monoid object asks for the same thing, but the \"set\" may be any object of a monoidal category and the multiplication is a morphism.\nThe laws are written as equalities of composite morphisms instead of equations between elements.\nFor example, a ring is an abelian group $R$ with a multiplication map $R \\otimes R \\to R$ that is associative and has a unit $1$: a monoid object in abelian groups.\n",
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