A free magma on a set is the "most general possible" magma generated by the set (that is there are no relations or axioms imposed on the generators; see free object). It can be described, in terms familiar in computer science, as the magma of binary trees with leaves labeled by elements of . The operation is that of joining trees at the root. It therefore has a foundational role in syntax.
A free magma has the universal property such that, if is a function from the set to any magma, then there is a unique extension of to a morphism of magmas
See also: free semigroup, free group, Hall set
Read more about this topic: Magma (algebra)
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