Monoid

In abstract algebra, a branch of mathematics, a monoid is a set equipped with an associative binary operation and an identity element. Monoids are semigroups with identity. Such algebraic structures occur in several branches of mathematics. For example, the functions from a set into itself form a monoid with respect to function composition. More generally, in category theory, the morphisms of an object to itself form a monoid, and, conversely, a monoid may be viewed as a category with a single object. See Semigroup for the history of the subject, and some other general properties of monoids.

Monoid

In abstract algebra, a branch of mathematics, a monoid is a set equipped with an associative binary operation and an identity element. Monoids are semigroups with identity. Such algebraic structures occur in several branches of mathematics. For example, the functions from a set into itself form a monoid with respect to function composition. More generally, in category theory, the morphisms of an object to itself form a monoid, and, conversely, a monoid may be viewed as a category with a single object. See Semigroup for the history of the subject, and some other general properties of monoids.