On the Functorialty of Stratified Desingularizations

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 [12]. In this paper we work with the category of Thom-Mather simple spaces [10], [14]. 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.