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. The sheaf of formal sections is interpreted as a fibrant replacement in the model structure.
There are two main results. The first result is that the category of continuous sheaves can embed in a model category. The class of cofibrations is not included in the category of continuous sheaves. However, the category of continuous sheaves has weak equivalences and fibrations. The second result is that the category of continuous sheaves has an ABC prefibration structure, a generalized structure of a model structure.