Hirsch describes in his Differential Topology the notion of a structure functor (page 52 of the first edition). Subsequently appears a Globalization Theorem involving such functors. The applications of this theorem suggested in this chapter of the book are to prove theorems 2.9, 2.12, and 2.13. However, as commented by Gustavo Granja in his comments on the book, it seems that this technique does not apply for 2.12 and 2.13.
Does anyone know about other applications of the globalization theorem in the literature (maybe even in the same book)?