# Category:Free Monoids

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This category contains results about Free Monoids.

Let $S$ be a set.

A **free monoid over $S$** is a monoid $M$ together with a mapping $i: S \to M$, subject to:

- For all monoids $N$, for all mappings $f: S \to N$, there is a unique monoid homomorphism $\bar f: M \to N$, such that:

- $\bar f \circ i = f$

This condition is called the **universal (mapping) property** or **UMP** of the **free monoid over $S$**.

Also included are free commutative monoids.

## Pages in category "Free Monoids"

This category contains only the following page.