Category:Free Monoids

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.