  H-principle (or homotopy principle) is the property that some solutions to a
partial differential equation/inequality can be obtained as a deformed of a
formal solution by a homotopy. Gromov defines the sheaf theoritic h-principle
in his book and shows the existence of h-principle from a very abstract
setting. In this paper, we clarify a categorical structure behind Gromov
h-principle. The main result is that a flexible sheaf can be understood as a
fibrant object in some categories.
