\begin{definition}[Definition:Monoid Category]
Let $\left({S, \circ}\right)$ be a monoid with identity $e_S$.
One can interpret $\left({S, \circ}\right)$ as being a category, with:
{{DefineCategory
| ob = Only one, say $*$
| mor = $a: * \to *$, for all $a \in S$
| comp =  $a \circ b: * \to *$ is defined using the operation $\circ$ of the monoid $S$
| id = $\operatorname{id}_* := e_S: * \to *$
}}
The category that so arises is called a '''monoid category'''.
{{expand|explanatory diagram}}
\end{definition}