  This article is devoted to the study of smooth desingularization, which are
customary employed in the definition of De Rham Intersection Cohomology with
differential forms. In this paper we work with the category of Thom-Mather
simple spaces. We construct a functor which sends each Thom-Mather simple space
into a smooth manifold called its primary unfolding. Hence we prove that the
primary unfoldings are unique up Thom-Mather isomorphisms.
