Monoids

Monoid

A monoid is a really simple concept which consists of a pair of set of objects $S$ and a binary operator $\cdot$ defined on them, such that

1. There exists an identity ($id \in S$) such that $a \cdot id = id \cdot a = a$ for all $a \in S$
2. The binary operator $\cdot$ is associative i.e. $a \cdot (b \cdot c) = (a \cdot b) \cdot c$ for all $a, b, c \in S$

Interesting note: Klesli Category can also be seen as a monoid with it’s morphisms as objects.