parsimony as a theoretical virtue alongside
descriptive accuracy, and aim to minimize the
amount of structure present in mathematical
formalisms used to represent physical systems. I
present a proposal for formalizing structure
comparison in physics using category theory,
which can be thought of as the mathematical
theory of structure. I show how this method can
be used to compare alternative formulations of
Yang-Mills theory (which underlies modern
particle physics), and evaluate claims by
philosophers and physicists regarding their
relative structure.