Metrization of free groups on ultrametric spaces

We consider ultrametrizations of free topological groups of ultrametric spaces. A construction is defined that determines a functor in the category UMET 1 of ultrametric spaces of diameter ⩽1 and nonexpanding maps. This functor is the functorial part of a monad in UMET 1 and we provide a characterization of the category of its algebras.