# đMonoid

In Category Theory, Monoid is a Category with one object.

\begin{tikzcd} m \arrow[loop, "f", distance=2em, leftarrow, swap] \arrow[loop, "g", distance=4em, leftarrow, swap] \arrow[loop, "g \circ f", distance=6em, leftarrow, swap] \end{tikzcd}

In Set Theory, Monoid is a set of values with

- an associative binary operator $*$
- a unit value $\exists e \ni \forall a.\; e * a = a = a *e$

These definitions are equivalent.

- set of values â set of morphisms
- associative binary operator â composition of morphisms
- unit value â identity morphism