Definition:Monoid Category

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Definition

Let $\struct {S, \circ}$ be a monoid with identity $e_S$.


One can interpret $\struct {S, \circ}$ as being a category, with:

Objects:         Only one, say $*$
Morphisms: $a: * \to *$, for all $a \in S$
Composition: $a \circ b: * \to *$ is defined using the operation $\circ$ of the monoid $S$
Identity morphisms: $\operatorname{id}_* := e_S: * \to *$

The category that so arises is called a monoid category.



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