On the Functoriality of Stratifled Desingularizations

This article is devoted to the study of smooth desingularizations, a geometric tool usually employed in the deflnition of the De Rham Intersection Cohomology with difierential 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, and prove that this construction is functorially preserved under Thom-Mather morphisms.