I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang–Mills theories. In particular, the chapter explains how the Baez–Bartel–Dolan framework for classifying forgetful functors provides a precise way of saying when one formulation of a physical theory posits more or less structure than another, and also when two theories posit equivalent amounts of structure.
On the reduction of general relativity to Newtonian gravitation