|Revista Colombiana de Matemáticas|
Abstract. A construction of colimits in the category of Hausdorff uniform spaces is carried out by means of a family of pseudometrics. Since this is not a topological category, its co-completeness can not be ensured by the standard procedures. A careful revision of the usual arguments is then required to this end.Palabras claves. Hausdorff uniform spaces, colimits, co-completeness.