A monoid is an algebraic structure with an identity value and an associative binary operation.
- Monoidal Identity
- The monoidal identity is the identity value for a particular monoid. A monoid must have an identity value and an associative binary operation. The identity value m is a value which makes no change to any other value n in that monoid, when n is combined with m using that binary operation.
- A category with a single object is a monoid
- A monoid has an associative binary operation
- The composition of morphisms in a monoidal category corresponds to an associative binary operation
- The identity morphism in a monoidal category corresponds to the unit element
- A set-theory monoid and a category-theory monoid are the same thing
- A monoid has a unit element