A Categorical Perspective on Symmetry and Equivalence
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In recent years, a number of authors have employed the resources of category theory to shed new light on the notion of ‘theoretical equivalence’. Here, we connect this work to the debate concerning the interpretational significance of symmetries in physics. Specifically, we put forward a novel criterion to be satisfied by any prospective ‘category of models’ of a scientific theory. This criterion is motivated primarily by the idea that the semantic representation of a theory should not include any redundant structure, and that redundant structure can be identified by representing the symmetries of a theory by auto-equivalences on the category of models of that theory.