Definition:Insertion of Generators

Definition

Let $S$ be a set, and let $S^*$ be its Kleene closure.

The insertion of generators (into $S^*$) is the mapping $i: S \to S^*$ defined by:

$i \left({s}\right) := \left\langle{s}\right\rangle$

that is, it sends any element $s$ of $S$ to the one-term sequence containing only $s$.

Also defined as

The mapping $i$ in the definition of a free monoid is also called insertion of generators.

From Kleene Closure is Free Monoid, we see that this viewpoint generalizes the definition given above.

Sources

• 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 1.7$