a closed half group with a neutral element

a semigroup that has an identity element

a semigroup with a unit

an abstract model of most situations in which a set of actions tend to change objects

In category theory, a monoid (or monoid object) (M,\mu,\eta) in a monoidal category C is an object M together with two morphisms

A set, M, defined on rational vectors, such that: (1) 0 is in M, and (2) if v, w are in M, then v+w is in M. The monoid is integral if it contains only integer vectors. One can think of a monoid as a discrete analogue of a convex cone.

a magma (M, ), i