Metrization of free groups on ultrametric spaces

Abstract

We consider ultrametrizations of free topological groups of ultrametric spaces. A construction is defined that determines a functor in the category UMET1 of ultrametric spaces of diameter ≤ 1 and nonexpanding maps. This functor is the functorial part of a monad in UMET1 and we provide a characterization of the category of its algebras