Fibration structure for Gromov h-principle

Abstract

The h-principle is a powerful tool for obtaining solutions to partial differential inequalities and partial differential equations. Gromov discovered the h-principle for the general partial differential relations to generalize the results of Hirsch and Smale. In his book, Gromov generalizes his theorem and discusses the sheaf theoretic h-principle, in which an object called a flexible sheaf plays an important role. We show that a flexible sheaf can be interpreted as a fibrant object with respect to a model structure.