Variational structure of infinite-dimensional homogeneous systems with dilations

This paper shows the variational structure of infinite-dimensional homogeneous systems. We rewrite homogeneities with dilations by a unified representation, called category theory. First, a homogeneous functor connecting dilations with homogeneities is defined. Next, introducing the variational problem in the jet bundle formalism, we can see that a homogeneous Lagrangian density determines infinite-dimensional homogeneous Euler-Lagrange equations.