Abstract

Category theory has become central to certain aspects of theoretical physics. Bain has recently argued that this has significance for ontic structural realism. We argue against this claim. In so doing, we uncover two pervasive forms of category-theoretic generalization. We call these ‘generalization by duality’ and ‘generalization by categorifying physical processes’. We describe in detail how these arise, and explain their significance using detailed examples. We show that their significance is two-fold: the articulation of high-level physical concepts, and the generation of new models. 1 Introduction2 Categories and Structuralism 2.1 Categories: abstract and concrete 2.2 Structuralism: simple and ontic3 Bain’s Two Strategies 3.1 A first strategy for defending Objectless 3.2 A second strategy for defending Objectless4 Two Forms of Categorical Generalization 4.1 Generalization by duality 4.2 Generalization by categorification 4.3 The role of category theory in physics5 Conclusion