Monoid

A monoid $(𝑀, \cdot)$ is a Semigroup with an identity element. #m/def/general In general elements needn't have an inverse.

Associative $𝑎 \cdot (𝑏 \cdot 𝑐) = (𝑎 \cdot 𝑏) \cdot 𝑐$ for each $𝑎, 𝑏, 𝑐 \in 𝑀$
Identity there exists (provably unique) $𝑒 \in 𝑀$ such that $𝑎 \cdot 𝑒 = 𝑒 \cdot 𝑎 = 𝑎$ for all $𝑎 \in 𝑀$

A monoid may be generalized to a category, which can be thought of as a typed monoid. See also Monoid object.

#state/develop | #lang/en | #SemBr